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Dissertations / Theses on the topic 'Stochastic Difference Equation'

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Published: 3 June 2025

Last updated: 31 July 2025

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1

Shedlock, Andrew James. "A Numerical Method for solving the Periodic Burgers' Equation through a Stochastic Differential Equation." Thesis, Virginia Tech, 2021. http://hdl.handle.net/10919/103947.

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The Burgers equation, and related partial differential equations (PDEs), can be numerically challenging for small values of the viscosity parameter. For example, these equations can develop discontinuous solutions (or solutions with large gradients) from smooth initial data. Aside from numerical stability issues, standard numerical methods can also give rise to spurious oscillations near these discontinuities. In this study, we consider an equivalent form of the Burgers equation given by Constantin and Iyer, whose solution can be written as the expected value of a stochastic differential eq

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2

Redmon, Jessica. "Stochastic Bubble Formation and Behavior in Non-Newtonian Fluids." Case Western Reserve University School of Graduate Studies / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case15602738261697.

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3

Zhou, Bo. "The existence of bistable stationary solutions of random dynamical systems generated by stochastic differential equations and random difference equations." Thesis, Loughborough University, 2009. https://dspace.lboro.ac.uk/2134/14255.

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In this thesis, we study the existence of stationary solutions for two cases. One is for random difference equations. For this, we prove the existence and uniqueness of the stationary solutions in a finite-dimensional Euclidean space Rd by applying the coupling method. The other one is for semi linear stochastic evolution equations. For this case, we follows Mohammed, Zhang and Zhao [25]'s work. In an infinite-dimensional Hilbert space H, we release the Lipschitz constant restriction by using Arzela-Ascoli compactness argument. And we also weaken the globally bounded condition for F by applyin

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4

Zanchini, Giulia. "Stochastic local volatility model for fx markets." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/7685/.

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Questa tesi verte sullo studio di un modello a volatilità stocastica e locale, utilizzato per valutare opzioni esotiche nei mercati dei cambio. La difficoltà nell'implementare un modello di tal tipo risiede nella calibrazione della leverage surface e uno degli scopi principali di questo lavoro è quello di mostrarne la procedura.

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5

Challa, Subhash. "Nonlinear state estimation and filtering with applications to target tracking problems." Thesis, Queensland University of Technology, 1998.

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6

Čajánek, Michal. "Modely stochastického programování v inženýrském návrhu." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2009. http://www.nusl.cz/ntk/nusl-228544.

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Two-stage stochastic programming problem with PDE constraint, specially elliptic equation is formulated. The computational scheme is proposed, whereas the emphasis is put on approximation techniques. We introduce method of approximation of random variables of stochastic problem and utilize suitable numerical methods, finite difference method first, then finite element method. There is also formulated a mathematical programming problem describing a membrane deflection with random load. It is followed by determination of the acceptableness of using stochastic optimization rather than determinist

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7

Jeisman, Joseph Ian. "Estimation of the parameters of stochastic differential equations." Thesis, Queensland University of Technology, 2006. https://eprints.qut.edu.au/16205/1/Joseph_Jesiman_Thesis.pdf.

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Stochastic di®erential equations (SDEs) are　central to much of modern finance theory and have been widely used to model the behaviour of key variables such as the　instantaneous short-term interest rate, asset prices, asset returns and their volatility.　The explanatory and/or predictive power of these models depends crucially on the particularisation of the model SDE(s) to real data through the choice of values for their parameters. In econometrics, optimal parameter estimates are generally considered to　be those that maximise the likelihood of the sample. In the context of the estimation of

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8

Jeisman, Joseph Ian. "Estimation of the parameters of stochastic differential equations." Queensland University of Technology, 2006. http://eprints.qut.edu.au/16205/.

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Stochastic di®erential equations (SDEs) are　central to much of modern finance theory and have been widely used to model the behaviour of key variables such as the　instantaneous short-term interest rate, asset prices, asset returns and their volatility.　The explanatory and/or predictive power of these models depends crucially on the particularisation of the model SDE(s) to real data through the choice of values for their parameters. In econometrics, optimal parameter estimates are generally considered to　be those that maximise the likelihood of the sample. In the context of the estimation of t

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9

Antar, Ezequiel. "Risk measures and financial innovation with backward stochastic difference/differential equations." Thesis, University of Cambridge, 2014. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708320.

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10

Roth, Jacob M. "The Explicit Finite Difference Method: Option Pricing Under Stochastic Volatility." Scholarship @ Claremont, 2013. http://scholarship.claremont.edu/cmc_theses/545.

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This paper provides an overview of the finite difference method and its application to approximating financial partial differential equations (PDEs) in incomplete markets. In particular, we study German’s [6] stochastic volatility PDE derived from indifference pricing. In [6], it is shown that the first order- correction to derivatives valued by indifference pricing can be computed as a function involving the stochastic volatility PDE itself. In this paper, we present three explicit finite difference models to approximate the stochastic volatility PDE and compare the resulting valuations to th

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11

Carvalho, Marcio Sousa. "Applying Perfect Simulation to solve stochastic difference equations that arise from certain time series models." Diss., Connect to online resource, 2005. http://wwwlib.umi.com/dissertations/fullcit/3165827.

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12

Pefferly, Robert J. "Finite difference approximations of second order quasi-linear elliptic and hyperbolic stochastic partial differential equations." Thesis, University of Edinburgh, 2001. http://hdl.handle.net/1842/11244.

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This thesis covers topics such as finite difference schemes, mean-square convergence, modelling, and numerical approximations of second order quasi-linear stochastic partial differential equations (SPDE) driven by white noise in less than three space dimensions. The motivation for discussing and expanding these topics lies in their implications in such physical phenomena as signal and information flow, gravitational and electromagnetic fields, large scale weather systems, and macro-computer networks. Chapter 2 delves into the hyperbolic SPDE in one space and one time dimension. This is an impo

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13

Hall, Eric Joseph. "Accelerated numerical schemes for deterministic and stochastic partial differential equations of parabolic type." Thesis, University of Edinburgh, 2013. http://hdl.handle.net/1842/8038.

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First we consider implicit finite difference schemes on uniform grids in time and space for second order linear stochastic partial differential equations of parabolic type. Under sufficient regularity conditions, we prove the existence of an appropriate asymptotic expansion in powers of the the spatial mesh and hence we apply Richardson's method to accelerate the convergence with respect to the spatial approximation to an arbitrarily high order. Then we extend these results to equations where the parabolicity condition is allowed to degenerate. Finally, we consider implicit finite difference a

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14

Kemajou, Elisabeth. "A Stochastic Delay Model for Pricing Corporate Liabilities." OpenSIUC, 2012. https://opensiuc.lib.siu.edu/dissertations/547.

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We suppose that the price of a firm follows a nonlinear stochastic delay differential equation. We also assume that any claim whose value depends on firm value and time follows a nonlinear stochastic delay differential equation. Using self-financed strategy and replication we are able to derive a random partial differential equation (RPDE) satisfied by any corporate claim whose value is a function of firm value and time. Under specific final and boundary conditions, we solve the RPDE for the debt value and loan guarantees within a single period and homogeneous class of debt. We then analyze th

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15

El-Fakharany, Mohamed Mostafa Refaat. "Finite Difference Schemes for Option Pricing under Stochastic Volatility and Lévy Processes: Numerical Analysis and Computing." Doctoral thesis, Universitat Politècnica de València, 2015. http://hdl.handle.net/10251/53917.

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[EN] In the stock markets, the process of estimating a fair price for a stock, option or commodity is consider the corner stone for this trade. There are several attempts to obtain a suitable mathematical model in order to enhance the estimation process for evaluating the options for short or long periods. The Black-Scholes partial differential equation (PDE) and its analytical solution, 1973, are considered a breakthrough in the mathematical modeling for the stock markets. Because of the ideal assumptions of Black-Scholes several alternatives have been developed to adequate the models to the

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16

Issoglio, Elena [Verfasser], Martina [Akademischer Betreuer] Zähle, Franco [Akademischer Betreuer] Flandoli, and Markus [Akademischer Betreuer] Riedle. "Stochastic partial differential equations with fractal noise : two different approaches / Elena Issoglio. Gutachter: Martina Zähle ; Franco Flandoli ; Markus Riedle." Jena : Thüringer Universitäts- und Landesbibliothek Jena, 2012. http://d-nb.info/1027706819/34.

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17

Ramirez, Jaime Hugo. "Optimal decisions in illiquid hedge funds." Thesis, University of Manchester, 2016. https://www.research.manchester.ac.uk/portal/en/theses/optimal-decisions-in-illiquid-hedge-funds(2147e116-7ac6-4a56-afe1-e45f482aa329).html.

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During the work of this research project we were interested in mathematical techniques that give us an insight to the following questions: How do we understand the trading decisions made by a manager of a hedge fund and what influences these decisions? In what way does an illiquid market affect these decisions and the performance of the fund? And how does the payment scheme affect the investor's decisions? Based on existing work on hedge fund management, we start with a fund that can be modelled with one risky investment and one riskless investment. Next, subject to the hedge fund special rewa

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18

Nguyen, Thi Quynh Giang. "Méthodes de Monte-Carlo pour les diffusions discontinues : application à la tomographie par impédance électrique." Thesis, Aix-Marseille, 2015. http://www.theses.fr/2015AIXM4342.

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Cette thèse porte sur le développement de méthodes de Monte-Carlo pour calculer des représentations Feynman-Kac impliquant des opérateurs sous forme divergence avec un coefficient de diffusion constant par morceaux. Les méthodes proposées sont des variantes de la marche sur les sphères à l'intérieur des zones avec un coefficient de diffusion constant et des techniques de différences finies stochastiques pour traiter les conditions aux interfaces aussi bien que les conditions aux limites de différents types. En combinant ces deux techniques, on obtient des marches aléatoires dont le score calcu

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19

Bénézet, Cyril. "Study of numerical methods for partial hedging and switching problems with costs uncertainty." Thesis, Université de Paris (2019-....), 2019. http://www.theses.fr/2019UNIP7079.

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Nous apportons dans cette thèse quelques contributions à l’étude théorique et numérique de certains problèmes de contrôle stochastique, ainsi que leurs applications aux mathématiques financières et à la gestion des risques financiers. Ces applications portent sur des problématiques de valorisation et de couverture faibles de produits financiers, ainsi que sur des problématiques réglementaires. Nous proposons des méthodes numériques afin de calculer efficacement ces quantités pour lesquelles il n’existe pas de formule explicite. Enfin, nous étudions les équations différentielles stochastiques r

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20

Chen, Zhuliang. "Numerical Methods for Optimal Stochastic Control in Finance." Thesis, 2008. http://hdl.handle.net/10012/3794.

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In this thesis, we develop partial differential equation (PDE) based numerical methods to solve certain optimal stochastic control problems in finance. The value of a stochastic control problem is normally identical to the viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation or an HJB variational inequality. The HJB equation corresponds to the case when the controls are bounded while the HJB variational inequality corresponds to the unbounded control case. As a result, the solution to the stochastic control problem can be computed by solving the corresponding HJB equation/variational

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21

DiTanna, Anthony Santino. "The optimal control of a Lévy process." 2009. http://hdl.handle.net/2152/6652.

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In this thesis we study the optimal stochastic control problem of the drift of a Lévy process. We show that, for a broad class of Lévy processes, the partial integro-differential Hamilton-Jacobi-Bellman equation for the value function admits classical solutions and that control policies exist in feedback form. We then explore the class of Lévy processes that satisfy the requirements of the theorem, and find connections between the uniform integrability requirement and the notions of the score function and Fisher information from information theory. Finally we present three different numerical

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22

Mudzimbabwe, Walter. "Pricing methods for Asian options." Thesis, 2010. http://hdl.handle.net/11394/3468.

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>Magister Scientiae - MSc<br>We present various methods of pricing Asian options. The methods include Monte Carlo simulations designed using control and antithetic variates, numerical solution of partial differential equation and using lower bounds.The price of the Asian option is known to be a certain risk-neutral expectation. Using the Feynman-Kac theorem, we deduce that the problem of determining the expectation implies solving a linear parabolic partial differential equation. This partial differential equation does not admit explicit solutions due to the fact that the distribution of a sum

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