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Janzon, Krister. "Monte Carlo Path Simulation and the Multilevel Monte Carlo Method." Thesis, Umeå universitet, Institutionen för fysik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-151975.
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A standard problem in the field of computational finance is that of pricing derivative securities. This is often accomplished by estimating an expected value of a functional of a stochastic process, defined by a stochastic differential equation (SDE). In such a setting the random sampling algorithm Monte Carlo (MC) is useful, where paths of the process are sampled. However, MC in its standard form (SMC) is inherently slow. Additionally, if the analytical solution to the underlying SDE is not available, a numerical approximation of the process is necessary, adding another layer of computational complexity to the SMC algorithm. Thus, the computational cost of achieving a certain level of accuracy of the estimation using SMC may be relatively high. In this thesis we introduce and review the theory of the SMC method, with and without the need of numerical approximation for path simulation. Two numerical methods for path approximation are introduced: the Euler–Maruyama method and Milstein's method. Moreover, we also introduce and review the theory of a relatively new (2008) MC method – the multilevel Monte Carlo (MLMC) method – which is only applicable when paths are approximated. This method boldly claims that it can – under certain conditions – eradicate the additional complexity stemming from the approximation of paths. With this in mind, we wish to see whether this claim holds when pricing a European call option, where the underlying stock process is modelled by geometric Brownian motion. We also want to compare the performance of MLMC in this scenario to that of SMC, with and without path approximation. Two numerical experiments are performed. The first to determine the optimal implementation of MLMC, a static or adaptive approach. The second to illustrate the difference in performance of adaptive MLMC and SMC – depending on the used numerical method and whether the analytical solution is available. The results show that SMC is inferior to adaptive MLMC if numerical approximation of paths is needed, and that adaptive MLMC seems to meet the complexity of SMC with an analytical solution. However, while the complexity of adaptive MLMC is impressive, it cannot quite compensate for the additional cost of approximating paths, ending up roughly ten times slower than SMC with an analytical solution.
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Lin, Xichen. "Monte Carlo Simulation and Integration." Scholarship @ Claremont, 2018. https://scholarship.claremont.edu/cmc_theses/2009.
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In this paper, we introduce the Tootsie Pop Algorithm and explore its use in different contexts. It can be used to estimate more general problems where a measure is defined, or in the context of statistics application, integration involving high dimensions. The Tootsie Pop Algorithm was introduced by Huber and Schott[2] The general process of Tootsie Pop Algorithm, just like what its name suggests, is a process of peeling down the outer shell, which is the larger enclosing set, to the center, which is the smaller enclosed. We obtain the average number of peels, which gives us an understanding of the ratio between the size of the shell and the size of the center. Each peel is generated by a random draw within the outer shell: if the drawn point is located in the center, we are done, else we update the outer shell such that the drawn point is right on its edge.
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Lee, Ming Ripman, and 李明. "Monte Carlo simulation for confined electrolytes." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31240513.
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Swetnam, Adam D. "Monte Carlo simulation of lattice polymers." Thesis, University of Warwick, 2011. http://wrap.warwick.ac.uk/49196/.
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The phase behaviour of lattice polymers and peptides, under various conditions, is investigated using Monte Carlo simulation. Wang-Landau sampling is used so that, in principle, phase diagrams can be determined from a single simulation. It is demonstrated that the pseudophase diagram for polymer molecules, in several environments, can be plotted when sampling only from the internal degrees of freedom, by determining an appropriate density of states. Several improvements to the simulation methods used are detailed. A new prescription for setting the modification factor in the Wang-Landau algorithm is described, tested and found, for homopolymers, to result in near optimum convergence throughout the simulation. Different methods of selecting moves from the pull move set are detailed, and their relative efficiencies determined. Finally, it is shown that results for a polymer in a slit with one attractive surface can be determined by sampling only from the internal degrees of freedom of a lattice polymer. Adsorption of lattice polymers and peptides is investigated by determining pseudophase diagrams for individual molecules. The phase diagram for a homopolymer molecule, near a surface with a pattern of interaction, is determined, with a pseudophase identified where the polymer is commensurate with the pattern. For an example lattice peptide, the existence of the new pseudophase is found to depend on whether both hydrophobic and polar beads are attracted to the surface. The phase diagram for a ring polymer under applied force, with variable solvent quality, is determined for the first time. The effect, on the phase diagram, of topological knots in the ring polymer is investigated. In addition to eliminating pseudophases where the polymer is flattened into a single layer, it is found that non-trivial knots result in additional pseudophases for tensile force.
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Lee, Ming Ripman. "Monte Carlo simulation for confined electrolytes /." Hong Kong : University of Hong Kong, 2000. http://sunzi.lib.hku.hk/hkuto/record.jsp?B22055009.
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Bryskhe, Henrik. "Optimization of Monte Carlo simulations." Thesis, Uppsala University, Department of Information Technology, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-121843.
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<p>This thesis considers several different techniques for optimizing Monte Carlo simulations. The Monte Carlo system used is Penelope but most of the techniques are applicable to other systems. The two mayor techniques are the usage of the graphics card to do geometry calculations, and raytracing. Using graphics card provides a very efficient way to do fast ray and triangle intersections. Raytracing provides an approximation of Monte Carlo simulation but is much faster to perform. A program was also written in order to have a platform for Monte Carlo simulations where the different techniques were implemented and tested. The program also provides an overview of the simulation setup, were the user can easily verify that everything has been setup correctly. The thesis also covers an attempt to rewrite Penelope from FORTAN to C. The new version is significantly faster and can be used on more systems. A distribution package was also added to the new Penelope version. Since Monte Carlo simulations are easily distributed, running this type of simulations on ten computers yields ten times the speedup. Combining the different techniques in the platform provides an easy to use and at the same time efficient way of performing Monte Carlo simulations.</p>
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Voegele, Simon. "Shortfall-Minimierung Theorie und Monte Carlo Simulation /." St. Gallen, 2007. http://www.biblio.unisg.ch/org/biblio/edoc.nsf/wwwDisplayIdentifier/02922300001/$FILE/02922300001.pdf.
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Jud, Andreas. "Monte-Carlo-Simulation einer Überstruktur auf Lipidmembranen." [S.l. : s.n.], 1998. http://www.diss.fu-berlin.de/1998/18/index.html.
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Yangthaisong, Anucha. "Monte Carlo simulation of silicon-germanium transistors." Thesis, Durham University, 2002. http://etheses.dur.ac.uk/4025/.
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Self-consistent Monte Carlo simulation studies of n-channel Si/SiGe modulation doped field effect transistors (MODFETs) and silicon-on-insulator lateral bipolar junction transistors (SOI- LBJTs) are reported in this thesis. As a preliminary to the device studies Monte Carlo simulations of electron transport in bulk Si strained as if grown on Si(_0.77)Ge(_0.23) and Si(_0.55)Ge(_0.45) substrates have been carried out at 300 K, for field strengths varied from 10(^4) to 2 x 10(^7) Vm(^-1). The calculations indicate an enhancement of the average electron drift velocity when Si is tensilely strained in the growth plane. The enhancement of electron velocity is more marked at low and intermediate electric fields, while at very high fields the velocity saturates at about the same value as unstrained Si. In addition the ensemble Monte Carlo method has been used to study the transient response to a stepped electric field of electrons in strained and unstrained Si. The calculations suggest that significant velocity overshoots occurs in strained material. Simulations of n-channel Si/Si(_1=z)Ge(_z) MODFETs with Ge fractions of 0.23, 0.25, and 0.45 have been performed. Five depletion mode devices with x = 0.23 and 0.25 were studied. The simulations provide information on the microscopic details of carrier behaviour, including carrier velocity, kinetic energy and carrier density, as a function of position in the device. Detailed time-dependent voltage signal analysis has been carried out to test device response and derive the frequency bandwidth. The simulations predict a current gain cut-off frequency of 60 ± 10 GHz for a device with a gate length of 0.07 /nm and a channel length of 0.25 um. Similar studies of depletion and enhancement mode n-channel Si/Sio.55Geo.45 MODFETs with a gate length of 0.18 /im have been carried out. Cut-off frequencies of 60 ±10 GHz and 90± 10 GHz are predicted for the depletion and enhancement mode devices respectively. A Monte Carlo model has also been devised and used to simulate steady state and transient electron and hole transport in SOI-LBJTs. Four devices have been studied and the effects of junction depth and silicon layer thickness have been investigated. The advantage of the silicon-on-insulator technology SOI device is apparent in terms of higher collector current, current gain, and cut-off frequency obtained in comparison with an all-silicon structure. The simulations suggest that the common-emitter current gain of the most promising SOI-LBJT structure considered could have a cut-off frequency approaching 35 ± 5 GHz.
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Mee, Richard A. W. "Monte Carlo simulation of step growth polymerization." Thesis, Queen's University Belfast, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318843.
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Lloyd, Jennifer A. "Numerical methods for Monte Carlo device simulation." Thesis, Massachusetts Institute of Technology, 1992. http://hdl.handle.net/1721.1/12766.
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Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1992.<br>Includes bibliographical references (leaves 51-53).<br>by Jennifer Anne Lloyd.<br>M.S.
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Joo, Balint. "Efficient Monte Carlo simulation of Lattice QCD." Thesis, University of Edinburgh, 1999. http://hdl.handle.net/1842/12319.
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This thesis is concerned with the efficient simulation of lattice QCD with dynamical fermions. We discuss two aspects of this theme, the tuning of existing algorithms and the investigation of novel algorithms. We begin with an introduction to lattice QCD and Monte Carlo Methods for its simulation. Particular emphasis is placed on the difficulties of the lattice formulation of fermion fields. We then continue with a description of the Hybrid Monte Carlo (HMC) algorithm, focusing on the conditions the algorithm must obey for correctness and on some of the numerical methods required for its implementation. We then discuss issues of reversibility and instability for the Molecular Dynamics part of HMC algorithm. After considering the source of instabilities in the context of free field theory we adopt a working hypothesis by which we can relate this instability to the case of lattice QCD. Our tuning studies of HMC attempt to investigate the behaviour of reversibility violations and simulation cost in the molecular dynamics with varying solver target residue <i>r.</i> We also investigate the onset of instabilities in the molecular dynamics while varying the solver residue <i>r</i> and the stepsize dt. Our second subject is the investigation of novel simulation algorithms. We consider the Parallel Tempering (PT) algorithm and its application to lattice QCD. We give an introduction to the algorithm and discuss the use of action matching technologies to tune the simulation parameters for maximal swap acceptance rates. We then discuss issues of cost for PT simulations by considering the CPU time needed by the algorithm for the estimation of the expectation value of an observable of interest and comparing this with the cost of reference HMC simulations. Finally we present some numerical results which indicate that we have a reasonable understanding of the algorithm but that we have not managed to maximise the acceptance rate through action matching. Due to large errors on our measured autocorrelation time we reserve judgements on the question of cost efficiency of the algorithm.
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Cunningham, Andrew Donald. "Monte Carlo simulation in the marine environment." Thesis, Liverpool John Moores University, 2011. http://researchonline.ljmu.ac.uk/6001/.
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Jensen, Mattias, and Mikael Westlund. "Monte Carlo-simulation of whole-body absorbed." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-276422.
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Radiation protection is important when working in lab environments where radioactive sources are frequently used. Simplified geometrical models are sometimes used in literature or in education to analytically estimate the absorbed dose a human receives. This study investigates the accuracy of these models by comparing them to more advanced models and how the results differ if the dose is simulated in Geant4. Three cuboids with different shapes, and two more human-like models were used as the bodies that would receive the absorbed dose. It turned out, for such simplified cases, that the result seemed to be a factor of 1.6 - 3 times larger than the results achieved in the Geant4 simulation. This result is a consequence of the Compton scattering that occurs when the photons enter the bodies, a process which the analytical method does not account for. It also turned out that besides using a more human-like model, the closest result was given when the cuboids surface area was reduced to get a more human-like weight instead of its thickness.<br>Strålskydd är viktigt inom jobbmiljöer där radioaktiva preparat förekommer ofta. Enkla geometriska modeller används ofta inom litteratur för att analytiskt uppskatta hur stor dos en person upptar. Den här rapporten diskuterar hur dessa modeller förhåller sig till mer avancerade modeller och hur annorlunda resultatet blir om dosen simuleras i Geant4. Tre rätblock med olika dimensioner och två mer människoliknande modeller har använts för att uppskatta den absorberande dosen. Det visade sig att resultatet var mellan 1.6 och 3 gånger större än resultatet som fås i Geant4simulationen. Detta är en konsekvens av Comptonspridningen som händer när en foton kommer in i kroppen och som inte tas hänsyn till i analytiska metoden. Det visade också sig att förutom de mer människoliknande modellerna så ges det bästa resultatet av att minska på rätblockets area istället för tjocklek för att rätblocket ska väga lika mycket som en människa.
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Kazeem, Funmilayo Eniola. "Multilevel Monte Carlo simulation in options pricing." University of the Western Cape, 2014. http://hdl.handle.net/11394/4349.
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>Magister Scientiae - MSc<br>In Monte Carlo path simulations, which are used extensively in computational -finance, one is interested in the expected value of a quantity which is a functional of the solution to a stochastic differential equation [M.B. Giles, Multilevel Monte
Carlo Path Simulation: Operations Research, 56(3) (2008) 607-617] where we have a scalar function with a uniform Lipschitz bound. Normally, we discretise the stochastic differential equation numerically. The simplest estimate for this expected value is the mean of the payoff (the value of an option at the terminal period) values from N independent path simulations. The multilevel Monte Carlo path simulation method recently introduced by Giles exploits strong convergence properties to improve the computational complexity by combining simulations with different levels of resolution. This new method improves on the computational complexity of the standard Monte Carlo approach by considering Monte Carlo simulations with a geometric sequence of different time steps following the approach of Kebaier [A. Kebaier, Statistical Romberg extrapolation: A new variance reduction method and applications to options pricing. Annals of Applied Probability 14(4) (2005) 2681- 2705]. The multilevel method makes computation easy as it estimates each of the terms of the estimate independently (as opposed to the Monte Carlo method) such that the computational complexity of Monte Carlo path simulations is minimised. In this thesis, we investigate this method in pricing path-dependent options and the computation of option price sensitivities also known as Greeks.
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Marshall, Timothy Craig. "KINETIC MONTE CARLO SIMULATION OF BINARY ALLOYS." VCU Scholars Compass, 2018. https://scholarscompass.vcu.edu/etd/5657.
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There are many tools to simulate physical phenomena. Generally, the simulation technique is defined by the size of the simulation area. Two well know techniques for simulating atom dynamics are kinetic Monte Carlo (kMC) and molecular dynamics (MD). In this work we simulate physical vapor deposition of binary metallic systems using the kMC technique. A sufficient quantity of atoms are deposited so that morphological features can be observed. Where kMC has fallen short we have used MD to supplement our results.
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Poole, Christopher Mark. "Faster Monte Carlo simulation of radiotherapy geometries." Thesis, Queensland University of Technology, 2012. https://eprints.qut.edu.au/59972/1/Christopher_Poole_Thesis.pdf.
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Using Monte Carlo simulation for radiotherapy dose calculation can provide more accurate results when compared to the analytical methods usually found in modern treatment planning systems, especially in regions with a high degree of inhomogeneity.
These more accurate results acquired using Monte Carlo simulation however, often require orders of magnitude more calculation time so as to attain high precision, thereby reducing its utility within the clinical environment. This work aims to improve the utility of Monte Carlo simulation within the clinical environment by developing techniques which enable faster Monte Carlo simulation of radiotherapy geometries. This is achieved principally through the use new high performance computing environments and simpler alternative, yet equivalent representations of complex geometries.
Firstly the use of cloud computing technology and it application to radiotherapy dose calculation is demonstrated. As with other super-computer like environments, the time to complete a simulation decreases as 1=n with increasing n cloud based computers performing the calculation in parallel. Unlike traditional super computer infrastructure however, there is no initial outlay of cost, only modest ongoing usage fees; the simulations described in the following are performed using this cloud computing technology. The definition of geometry within the chosen Monte Carlo simulation environment - Geometry & Tracking 4 (GEANT4) in this case - is also addressed in this work. At the simulation implementation level, a new computer aided design interface is presented for use with GEANT4 enabling direct coupling between manufactured parts and their equivalent in the simulation environment, which is of particular importance when defining linear accelerator treatment head geometry. Further, a new technique for navigating tessellated or meshed geometries is described, allowing for up to 3 orders of magnitude performance improvement with the use of tetrahedral meshes in place of complex triangular surface meshes. The technique has application in the definition of both mechanical parts in a geometry as well as patient geometry.
Static patient CT datasets like those found in typical radiotherapy treatment plans are often very large and present a significant performance penalty on a Monte Carlo simulation. By extracting the regions of interest in a radiotherapy treatment plan, and representing them in a mesh based form similar to those used in computer aided design, the above mentioned optimisation techniques can be used so as to reduce the time required to navigation the patient geometry in the simulation environment. Results presented in this work show that these equivalent yet much simplified patient geometry representations enable significant performance improvements over simulations that consider raw CT datasets alone.
Furthermore, this mesh based representation allows for direct manipulation of the geometry enabling motion augmentation for time dependant dose calculation for example. Finally, an experimental dosimetry technique is described which allows the validation of time dependant Monte Carlo simulation, like the ones made possible by the afore mentioned patient geometry definition. A bespoke organic plastic scintillator dose rate meter is embedded in a gel dosimeter thereby enabling simultaneous 3D dose distribution and dose rate measurement.
This work demonstrates the effectiveness of applying alternative and equivalent geometry definitions to complex geometries for the purposes of Monte Carlo simulation performance improvement. Additionally, these alternative geometry definitions allow for manipulations to be performed on otherwise static and rigid geometry.
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Tuffin, Bruno. "Simulation acceleree par les methodes de monte carlo et quasi-monte carlo : theorie et applications." Rennes 1, 1997. http://www.theses.fr/1997REN10181.
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Dans cette these nous etudions et appliquons les methodes de monte carlo et quasi-monte carlo. Nous nous interessons premierement a la theorie. Les methodes de quasi-monte carlo sont basees sur deux notions : la variation et la discrepance. Comme premiere contribution, nous ameliorons la repartition d'une famille importante de suites a discrepance faible, les suites de halton. Nous realisons ensuite une technique analogue a la reduction de la variance dans les methodes de monte carlo, la reduction de la variation. La borne de l'erreur n'etant que rarement utilisable en pratique, nous proposons une approche pour l'utilisation des suites a discrepance faible comme technique de reduction de la variance dans les methodes de monte carlo. Nous analysons l'efficacite de cette reduction et comparons les differentes suites afin de choisir la mieux adaptee. La deuxieme partie de la these est consacree a des applications concretes et efficaces de ces methodes. Nous considerons d'abord les reseaux de files d'attente multi-classes a forme produit et ameliorons leur simulation par deux techniques differentes de reduction de la variance : les variables antagonistes et les suites a discrepance faible. Cette derniere methode est ensuite appliquee a la simulation d'un systeme cellulaire avec partage dynamique des ressources. Finalement, nous etudions la simulation des systemes markoviens hautement fiables et approfondissons les methodes existantes. Nous introduisons un nouveau concept, l'approximation normale bornee, qui permet d'obtenir une approximation de la loi normale satisfaisante dans le theoreme de la limite centrale, quelle que soit la fiabilite du systeme etudie, et donnons une condition necessaire et suffisante sur la mesure d'echantillonnage preferentiel pour obtenir cette propriete.
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Jaeckel, Alain. "Simulations Monte Carlo de chaînes confinées." Montpellier 2, 1997. http://www.theses.fr/1997MON20206.
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Par simulation monte carlo (smc), nous generons a l'ordinateur des chemins statistiques (rfws) ou auto-evitants (saws) a l'interieur de pores spheriques de rayons variables. Ces chemins modelisent respectivement des chaines polymere confinees en solvant theta et en bon solvant. A partir des chaines ainsi construites, on estime les dimensions moyennes usuelles (distance moyenne bout a bout et rayon de giration moyen), les distributions des milieux et des extremites ou tous maillons confondus dans la sphere de confinement, la variation d'entropie en fonction du confinement impose et enfin la pression exercee par la chaine sur la surface de confinement. Nous donnons egalement une relation universelle entre le nombre de conformations d'une chaine de n pas, quel que soit son type, et un parametre de compacite determine par smc. Nous proposons aussi une extension de la theorie des blobs de de gennes. Nous discutons nos resultats au vu de resultats theoriques ou de publications anterieures. Nous etablissons l'existence de lois d'echelle, moyennant l'utilisation de parametres de reduction specifiques a chaque type de chaines (rfws ou saws), et montrons que rfws et saws presentent des comportements comparables pour des valeurs egales du rayon reduit de la sphere de confinement. Ainsi, certaines proprietes des saws confines dans des spheres peuvent etre deduits des resultats theoriques plus accessibles des rfws confines en tenant compte d'une simple renormalisation des dimensions, et ce avec un degre d'approximation satisfaisant, voire bon. Nous etendons nos smc au cas des parcours hamiltoniens dont le nombre peut etre estime, pour un carre de cote donne, via l'utilisation d'une loi d'echelle empirique que nous avons etablie. Enfin, nous avons cherche a elucider un vieux probleme de la litterature qui concerne l'exposant d'echelle et la dimension critique des chaines auto-evitantes generees par la procedure reflechissante non ponderee de rosenbluth et rosenbluth.
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Kunert, Roland. "Monte Carlo simulation of stacked quantum dot arrays." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=981321399.
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Hanlon, Peter E. "A retirement planning model using Monte Carlo simulation." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2000. http://handle.dtic.mil/100.2/ADA386389.
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Coskuner, Orkide. "Investigation of hydrophobic interactions by Monte Carlo simulation." [S.l. : s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=968831664.
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Can, Mutan Oya. "Comparison Of Regression Techniques Via Monte Carlo Simulation." Master's thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/3/12605175/index.pdf.
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The ordinary least squares (OLS) is one of the most widely used methods for modelling the functional relationship between variables. However, this estimation procedure counts on some assumptions and the violation of these assumptions may lead to nonrobust estimates. In this study, the simple linear regression model is investigated for conditions in which the distribution of the error terms is Generalised Logistic. Some robust and nonparametric methods such as modified maximum likelihood (MML), least absolute deviations (LAD), Winsorized least squares, least trimmed squares (LTS), Theil and weighted Theil are compared via computer simulation. In order to evaluate the estimator performance, mean, variance, bias, mean square error (MSE) and relative mean square error (RMSE) are computed.
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Dahlgren, Ronnie. "Monte Carlo Simulation of Light Scattering in Paper." Thesis, Linköpings universitet, Institutionen för teknik och naturvetenskap, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-97857.
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Paper is a very complex optical material. Analytical models explaining some of the optical properties of mpaper exist, but they often rely on bold simplifications. Monte Carlo simulation models are less constrained and allow for a greater degree of complexity. Grace is a three-dimensional light scattering simulation tool for paper, previously implemented in Matlab. During this project, the basesheet model was implemented in C++. This model simulates a layer containing a network of wood fibers and filler material. The new implementation makes simulations much faster. In addition, some new features and enhancements were developed. Wavelength dependency of parameters and fluorescence were implemented and tested. A problem with Grace was that there was no simple way to calculate the grammage of the simulated paper. A method to analytically determine grammage was developed so that the user has complete control over the grammage of the fiber network. Modifications were made to improve light scattering at the pore boundaries. A new feature was also added to study how the fibers’ and fillers’ geometry affects the light scattering at the paper surface.
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Suzuki, Yuya. "Rare-event Simulation with Markov Chain Monte Carlo." Thesis, KTH, Matematisk statistik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-138950.
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In this thesis, we consider random sums with heavy-tailed increments. By the term random sum, we mean a sum of random variables where the number of summands is also random. Our interest is to analyse the tail behaviour of random sums and to construct an efficient method to calculate quantiles. For the sake of efficiency, we simulate rare-events (tail-events) using a Markov chain Monte Carlo (MCMC) method. The asymptotic behaviour of sum and the maximum of heavy-tailed random sums is identical. Therefore we compare random sum and maximum value for various distributions, to investigate from which point one can use the asymptotic approximation. Furthermore, we propose a new method to estimate quantiles and the estimator is shown to be efficient.
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Wu, Yun-Fu. "Monte Carlo simulation studies of mechanical system reliabilities." Thesis, University of Cambridge, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.259553.
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Gudmundsson, Thorbjörn. "Rare-event simulation with Markov chain Monte Carlo." Doctoral thesis, KTH, Matematisk statistik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-157522.
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Stochastic simulation is a popular method for computing probabilities or expecta- tions where analytical answers are difficult to derive. It is well known that standard methods of simulation are inefficient for computing rare-event probabilities and there- fore more advanced methods are needed to those problems. This thesis presents a new method based on Markov chain Monte Carlo (MCMC) algorithm to effectively compute the probability of a rare event. The conditional distri- bution of the underlying process given that the rare event occurs has the probability of the rare event as its normalising constant. Using the MCMC methodology a Markov chain is simulated, with that conditional distribution as its invariant distribution, and information about the normalising constant is extracted from its trajectory. In the first two papers of the thesis, the algorithm is described in full generality and applied to four problems of computing rare-event probability in the context of heavy- tailed distributions. The assumption of heavy-tails allows us to propose distributions which approximate the conditional distribution conditioned on the rare event. The first problem considers a random walk Y1 + · · · + Yn exceeding a high threshold, where the increments Y are independent and identically distributed and heavy-tailed. The second problem is an extension of the first one to a heavy-tailed random sum Y1+···+YN exceeding a high threshold,where the number of increments N is random and independent of Y1 , Y2 , . . .. The third problem considers the solution Xm to a stochastic recurrence equation, Xm = AmXm−1 + Bm, exceeding a high threshold, where the innovations B are independent and identically distributed and heavy-tailed and the multipliers A satisfy a moment condition. The fourth problem is closely related to the third and considers the ruin probability for an insurance company with risky investments. In last two papers of this thesis, the algorithm is extended to the context of light- tailed distributions and applied to four problems. The light-tail assumption ensures the existence of a large deviation principle or Laplace principle, which in turn allows us to propose distributions which approximate the conditional distribution conditioned on the rare event. The first problem considers a random walk Y1 + · · · + Yn exceeding a high threshold, where the increments Y are independent and identically distributed and light-tailed. The second problem considers a discrete-time Markov chains and the computation of general expectation, of its sample path, related to rare-events. The third problem extends the the discrete-time setting to Markov chains in continuous- time. The fourth problem is closely related to the third and considers a birth-and-death process with spatial intensities and the computation of first passage probabilities. An unbiased estimator of the reciprocal probability for each corresponding prob- lem is constructed with efficient rare-event properties. The algorithms are illustrated numerically and compared to existing importance sampling algorithms.<br><p>QC 20141216</p>
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Kundu, Ashoke. "Monte Carlo simulation of gas-filled radiation detectors." Thesis, University of Surrey, 2000. http://epubs.surrey.ac.uk/987/.
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Ma, Chang Ming. "Monte Carlo simulation of dosimeter response using transputers." Thesis, Institute of Cancer Research (University Of London), 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.287080.
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Sadi, Toufik. "Electrothermal Monte Carlo simulation heterostructure field-effect transistors." Thesis, University of Leeds, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.445359.
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BURBAN, PIERRE ALEXANDRE CHARLES. "PRICING OF EXOTICS OPTIONS: USING MONTE-CARLO SIMULATION." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2008. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=11901@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>As opções financeiras são instrumentos derivativos cada dia
mais usados
na gestão de risco de mercado das empresas e dos
investidores. Dependendo do
tipo e das características da opção escolhida, geralmente
não existem soluções
analíticas ao problema de apreçamento do instrumento. A
simulação de Monte-
Carlo é um método que, aplicado ao problema de apreçamento,
possibilita uma
grande flexibilidade na integração das variáveis de cálculo
e uma precisão que
depende do número de simulações efetuadas. As opções
exóticas têm
características especiais e seus valores podem ser
estimados com precisão
aplicando as técnicas de simulação. Esta dissertação propõe
uma abordagem e
aplica técnicas de cálculo no apreçamento das opções
exóticas mais
freqüentemente encontradas nos mercados de capitais. Os
algoritmos
desenvolvidos podem ser usados no estudo e valoração de
casos reais.<br>Financial options are derivatives tools each day more and
more used in
market and enterprise risk control systems. Depending on
the option type used, it
doesn`t have an analytical solution for the pricing
problem. A Monte-Carlo
simulation is a very flexible method, which applied to the
pricing problem, allows
very-easy new variable implementation and accuracy increase
with the number of
simulation done. Exotics options have special features and
pricing them by this
method gives accurate results. Thus, this study explores a
pricing solution and
applied techniques of quite common exotics options traded
on the market. The
algorithms developed can be used for pricing real cases.
32
Nail, Graeme. "Quantum chromodynamics : simulation in Monte Carlo event generators." Thesis, University of Manchester, 2018. https://www.research.manchester.ac.uk/portal/en/theses/quantum-chromodynamics-simulation-in-monte-carlo-event-generators(46dc6f2e-1552-4dfa-b435-9608932a3261).html.
Full textAbstract:
This thesis contains the work of two recent developments in the Herwig general purpose event genrator. Firstly, the results from an new implementation of the KrkNLO method in the Herwig event generator are presented. This method allows enables the generation of matched next-to-leading order plus parton shower events through the application of simple positive weights to showered leading order events. This simplicity is achieved by the construction Monte Carlo scheme parton distribution functions. This implementation contains the necessary components to simulation Drell-Yan production as well as Higgs production via gluon fusion. This is used to generate the first differential Higgs results using this method. The results from this implementation are shown to be comparable with predictions from the well established approaches of POWHEG and MC@NLO. The predictions from KrkNLO are found to closely resemble the original configuration for POWHEG. Secondly, a benchmark study focussing on the source of perturbative uncertainties in parton showers is presented. The study employs leading order plus parton shower simulations as a starting point in order to establish a baseline set of controllable uncertainties. The aim of which is to build an understanding of the uncertainties associated with a full simulation which includes higher-order corrections and interplay with non- perturbative models. The uncertainty estimates for a number of benchmark processes are presented. The requirement that these estimates be consistent across the two distinct parton show implementations in Herwig provided an important measure to assess the quality of these uncertainty estimates. The profile scale choice is seen to be an important consideration with the power and hfact displaying inconsistencies between the showers. The resummation profile scale is shown to deliver consistent predictions for the central value and uncertainty bands.
33
Tari, Ilker. "Homogenized cross section determination using Monte Carlo simulation." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/28054.
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34
Blanckenberg, J. P. (Jacobus Petrus). "Monte Carlo simulation of direction sensitive antineutrino detection." Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/2885.
Full textAbstract:
Thesis (MSc (Physics))--University of Stellenbosch, 2010.<br>ENGLISH ABSTRACT:
Neutrino and antineutrino detection is a fairly new eld of experimental physics,
mostly due to the small interaction cross section of these particles. Most of
the detectors in use today are huge detectors consisting of kilotons of scintilator
material and large arrays of photomultiplier tubes. Direction sensitive
antineutrino detection has however, not been done (at the time of writing of
this thesis). In order to establish the feasibility of direction sensitive antineutrino
detection, a Monte Carlo code, DSANDS, was written to simulate the
detection process. This code focuses on the neutron and positron (the reaction
products after capture on a proton) transport through scintilator media. The
results are then used to determine the original direction of the antineutrino,
in the same way that data from real detectors would be used, and to compare
it with the known direction. Further investigation is also carried out into the
required amount of statistics for accurate results in an experimental eld where
detection events are rare. Results show very good directional sensitivity of the
detection method.<br>AFRIKAANSE OPSOMMING:
Neutrino en antineutrino meting is 'n relatief nuwe veld in eksperimentele sika,
hoofsaaklik as gevolg van die klein interaksie deursnee van hierdie deeltjies. Die
meeste hedendaagse detektors is massiewe detektors met kilotonne sintilator
materiaal en groot aantalle fotovermenigvuldiger buise. Tans is rigting sensitiewe
antineutrino metings egter nog nie uit gevoer nie. 'n Monte Carlo kode,
DSANDS, is geskryf om die meet proses te simuleer en sodoende die uitvoerbaarheid
van rigting sensitiewe antineutrino metings vas te stel. Hierdie kode
fokus op die beweging van neutrone en positrone (die reaksie produkte) deur
die sintilator medium. Die resultate word dan gebruik om die oorspronklike
rigting van die antineutrino te bepaal, soos met data van regte detektors gedoen
sou word, en te vergelyk met die bekende oorspronklike rigting van die
antineutrino. Verder word daar ook gekyk na die hoeveelheid statistiek wat
nodig sal wees om akkurate resultate te kry in 'n veld waar metings baie skaars
is. Die resultate wys baie goeie rigting sensitiwiteit van die meet metode.
35
Persson, Joakim. "Diagrammatic Monte Carlo Simulation of the Polaron Problem." Thesis, KTH, Teoretisk fysik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-188831.
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36
Stephen, Alexander. "Enhancement of thermionic cooling using Monte Carlo simulation." Thesis, University of Aberdeen, 2014. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=210113.
Full textAbstract:
Advances in the field of semiconductor physics have allowed for rapid development of new, more powerful devices. The new fabrication techniques allow for reductions in device geometry, increasing the possible wafer packing density. The increased output power comes with the price of excessive heat generation, the removal of which proves problematic at such scales for conventional cooling systems. Consequently, there is a rising demand for new cooling systems, preferably those that do not add large amount of additional bulk to the system. One promising system is the thermoelectric (TE) cooler which is small enough to be integrated onto the device wafer. Unlike more traditional gas and liquid coolers, TE coolers do not require moving parts or external liquid reservoirs, relying only on the flow of electrons to transport heat energy away from the device. Although TE cooling provides a neat solution for the extraction of heat from micron scale devices, it can normally only produce small amounts of cooling of 1-2 Kelvin, limiting its application to low power devices. This research aimed to find ways to enhance the performance of the TE cooler using detailed simulation analysis. For this, a self consistent, semi-classical, ensemble Monte Carlo model was designed to investigate the operation of the TE cooler at a higher level than would be possible with experimental measurements alone. As part of its development, the model was validated on a variety of devices including a Gunn diode and two micro-cooler designs from the literature, one which had been previously simulated and another which had been experimentally analysed. When applied to the TE cooler of focus, novel operational data was obtained and signification improvements in cooling power were found with only minor alterations to the device structure and without need for an increase in volume.
37
Ventura, Marcelo dos Santos. "Monte Carlo simulation studies in log-symmetric regressions." Universidade Federal de Goiás, 2018. http://repositorio.bc.ufg.br/tede/handle/tede/8278.
Full textAbstract:
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Previous issue date: 2018-03-09<br>Fundação de Amparo à Pesquisa do Estado de Goiás - FAPEG<br>This work deals with two Monte Carlo simulation studies in log-symmetric regression models,
which are particularly useful for the cases when the response variable is continuous, strictly
positive and asymmetric, with the possibility of the existence of atypical observations. In log-
symmetric regression models, the distribution of the random errors multiplicative belongs to
the log-symmetric class, which encompasses log-normal, log- Student-t, log-power-
exponential, log-slash, log-hyperbolic distributions, among others. The first simulation study
has as objective to examine the performance for the maximum-likelihood estimators of the
model parameters, where various scenarios are considered. The objective of the second
simulation study is to investigate the accuracy of popular information criteria as AIC, BIC,
HQIC and their respective corrected versions. As illustration, a movie data set obtained and
assembled for this dissertation is analyzed to compare log-symmetric models with the normal
linear model and to obtain the best model by using the mentioned information criteria.<br>Este trabalho aborda dois estudos de simulação de Monte Carlo em modelos de regressão log-
simétricos, os quais são particularmente úteis para os casos em que a variável resposta é
contínua, estritamente positiva e assimétrica, com possibilidade da existência de observações
atípicas. Nos modelos de regressão log-simétricos, a distribuição dos erros aleatórios
multiplicativos pertence à classe log-simétrica, a qual engloba as distribuições log-normal,
log-Student- t, log-exponencial- potência, log-slash, log-hyperbólica, entre outras. O primeiro
estudo de simulação tem como objetivo examinar o desempenho dos estimadores de máxima
verossimilhança desses modelos, onde vários cenários são considerados. No segundo estudo
de simulação o objetivo é investigar a eficácia critérios de informação populares como AIC,
BIC, HQIC e suas respectivas versões corrigidas. Como ilustração, um conjunto de dados de
filmes obtido e montado para essa dissertação é analisado para comparar os modelos de
regressão log-simétricos com o modelo linear normal e para obter o melhor modelo utilizando
os critérios de informação mencionados.
38
Hanson, Cole Thomas. "Valuing Origin Switching Options Using Monte Carlo Simulation." Thesis, North Dakota State University, 2020. https://hdl.handle.net/10365/31821.
Full textAbstract:
Commodity trading firms work to remain competitive in the evolving agricultural industry. They work to become more efficient by increasing economies of size and scale, vertically and horizontally integrating, and diversifying geographically, or any combination of these avenues. Geographically diverse firms have access to multiple origins between which, spatial arbitrage opportunities can occur. When spatial arbitrage opportunities occur, firms take advantage of them to generate profit. Origin switching options are one way to take advantage of these opportunities. Origin switching option allow the seller of grain to fill a contract with any listed origin at the cost of the premium negotiated. This thesis helps to determine the value of these origin type switching options by developing a Monte Carlo simulation model with real option analysis. Soybean and corn markets are analyzed in the U.S. Gulf, Pacific Northwest, Brazil, Argentine, and origins with China and Japan as the respective destinations.
39
Abdolsalami, Farzan. "Monte Carlo simulation of high field transport equations /." The Ohio State University, 1989. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487671108304647.
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40
Colakovic, Sabina, and Viktor Ågren. "Multilevel Monte Carlo Simulation for American Option Pricing." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-54356.
Full textAbstract:
In this thesis, we center our research around the analytical approximation of American put options with the Multilevel Monte Carlo simulation approach. The focus lies on reducing the computational complexity of estimating an expected value arising from a stochastic differential equation. Numerical results showcase that the simulations are consistent with the theoretical order of convergence of Monte Carlo simulations. The approximations are accurate and considerately more computationally efficient than the standard Monte Carlo simulation method.
41
Schöön, Jonathan. "Pricing Put Options with Multilevel Monte Carlo Simulation." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-55404.
Full textAbstract:
Monte Carlo path simulations are common in mathematical and computational finance as a way of estimating the expected values of a quantity such as a European put option, which is functional to the solution of a stochastic differential equation (SDE). The computational complexity of the standard Monte Carlo (MC) method grows quite large quickly, so in this thesis we focus on the Multilevel Monte Carlo (MLMC) method by Giles, which uses multigrid ideas to reduce the computational complexity. We use a Euler-Maruyama time discretisation for the approximation of the SDE and investigate how the convergence rate of the MLMC method improves the computational times and cost in comparison with the standard MC method. We perform a numerical analysis on the computational times and costs in order to achieve the desired accuracy and present our findings on the performance of the MLMC method on a European put option compared to the standard MC method.
42
Steinke, Tanja. "Ein Monte-Carlo-Modell zur Simulation plasmagespritzter Wärmedämmschichten /." Tönning ; Lübeck Marburg : Der Andere Verl, 2008. http://d-nb.info/989939944/04.
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Junnarkar, Parikshit Manoj. "Monte-Carlo simulation of photoproduction of Omega meson." Master's thesis, Mississippi State : Mississippi State University, 2006. http://library.msstate.edu/etd/show.asp?etd=etd-07312006-013358.
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44
Jackson, Andrew N. "Structural phase behaviour via Monte Carlo techniques." Thesis, University of Edinburgh, 2001. http://hdl.handle.net/1842/4850.
Full textAbstract:
There are few reliable computational techniques applicable to the problem of structural phase behaviour. This is starkly emphasised by the fact that there are still a number of unanswered questions concerning the solid state of some of the simplest models of matter. To determine the phase behaviour of a given system we invoke the machinery of statistical physics, which identifies the equilibrium phase as that which minimises the free-energy. This type of problem can only be dealt with fully via numerical simulation, as any less direct approach will involve making some uncontrolled approximation. In particular, a numerical simulation can be used to evaluate the free-energy difference between two phases if the simulation is free to visit them both. However, it has proven very difficult to find an algorithm which is capable of efficiently exploring two different phases, particularly when one or both of them is a crystalline solid. This thesis builds on previous work (Physical Review Letters 79 p.3002), exploring a new Monte Carlo approach to this class of problem. This new simulation technique uses a global coordinate transformation to switch between two different crystalline structures. Generally, this `lattice switch' is found to be extremely unlikely to succeed in a normal Monte Carlo simulation. To overcome this, extended-sampling techniques are used to encourage the simulation to visit `gateway' microstates where the switch will be successful. After compensating for this bias in the sampling, the free-energy difference between the two structures can be evaluated directly from their relative probabilities. As concrete examples on which to base the research, the lattice-switch Monte Carlo method is used to determine the free-energy difference between the face-centred cubic (fcc) and hexagonal close-packed (hcp) phases of two generic model systems --- the hard-sphere and Lennard-Jones potentials. The structural phase behaviour of the hard-sphere solid is determined at densities near melting and in the close-packed limit. The factors controlling the efficiency of the lattice-switch approach are explored, as is the character of the `gateway' microstates. The face-centred cubic structure is identified as the thermodynamically stable phase, and the free-energy difference between the two structures is determined with high precision. These results are shown to be in complete agreement with the results of other authors in the field (published during the course of this work), some of whom adopted the lattice-switch method for their calculations. Also, the results are favourably compared against the experimentally observed structural phase behaviour of sterically-stabilised colloidal dispersions, which are believed to behave like systems of hard spheres. The logical extension of the hard sphere work is to generalise the lattice-switch technique to deal with `softer' systems, such as the Lennard-Jones solid. The results in the literature for the structural phase behaviour of this relatively simple system are found to be completely inconsistent. A number of different approaches to this problem are explored, leading to the conclusion that these inconsistencies arise from the way in which the potential is truncated. Using results for the ground-state energies and from the harmonic approximation, we develop a new truncation scheme which allows this system to be simulated accurately and efficiently. Lattice-switch Monte Carlo is then used to determine the fcc-hcp phase boundary of the Lennard-Jones solid in its entirety. These results are compared against the experimental results for the Lennard-Jones potential's closest physical analogue, the rare-gas solids. While some of the published rare-gas observations are in approximate agreement with the lattice-switch results, these findings contradict the widely held belief that fcc is the equilibrium structure of the heavier rare-gas solids for all pressures and temperatures. The possible reasons for this disagreement are discussed. Finally, we examine the pros and cons of the lattice-switch technique, and explore ways in which it can be extended to cover an even wider range of structures and interactions.
45
Fan, Yanan. "Efficient implementation of Markov chain Monte Carlo." Thesis, University of Bristol, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.343307.
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46
Ye, Haocheng. "Monte Carlo Methods in Option Pricing." Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/cmc_theses/2122.
Full textAbstract:
This article investigates several variance reduction techniques in Monte Carlo simulation applied in option pricing. It first shows how Monte Carlo simulation could be leveraged in the field of option pricing by demonstrating the quality of Monte Carlo methods and properties of stock options. Then the articles simulate stock price trajectories to infer the optimal option price by averaging the payoff at maturity. The article shows in depth the effect of control variates and antithetic variates, and importance sampling in reducing variance. The last part of the article shows how the same variance reduction techniques could be used in more exotic options such as Asian and Bermuda options. In these cases, their closed-form expressions are more difficult to derive compared to the European options, and thus simulation is widely practiced in the industry.
47
Wang, Dong-Mei. "Monte Carlo simulations for complex option pricing." Thesis, University of Manchester, 2010. https://www.research.manchester.ac.uk/portal/en/theses/monte-carlo-simulations-for-complex-option-pricing(a908ec86-2fb2-4d5d-83e5-9bff78033edd).html.
Full textAbstract:
The thesis focuses on pricing complex options using Monte Carlo simulations. Due to the versatility of the Monte Carlo method, we are able to evaluate option prices with various underlying asset models: jump diffusion models, illiquidity models, stochastic volatility and so on. Both European options and Bermudan options are studied in this thesis.For the jump diffusion model in Merton (1973), we demonstrate European and Bermudan option pricing by the Monte Carlo scheme and extend this to multiple underlying assets; furthermore, we analyse the effect of stochastic volatility.For the illiquidity model in the spirit of Glover (2008), we model the illiquidity impact on option pricing in the simulation study. The four models considered are: the first order feedback model with constant illiquidity and stochastic illiquidity; the full feedback model with constant illiquidity and stochastic illiquidity. We provide detailed explanations for the present of path failures when simulating the underlying asset price movement and suggest some measures to overcome these difficulties.
48
Furrer, Marc. "Numerical Accuracy of Least Squares Monte Carlo." St. Gallen, 2008. http://www.biblio.unisg.ch/org/biblio/edoc.nsf/wwwDisplayIdentifier/01650217002/$FILE/01650217002.pdf.
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Reichert, Michael. "Monte-Carlo-Simulationen zum Clustermodell der Quasikristalle." [S.l. : s.n.], 2001. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB9716181.
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Haryanto, Freddy. "Monte-Carlo-Simulation des Strahlungstransports im Strahlerkopf eines Elektronenlinearbeschleunigers." [S.l. : s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=968559891.
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