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Journal articles on the topic 'Méthodes de quasi Monte Carlo'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

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1

Faure, Henri. "Méthodes quasi-Monte-Carlo multidimensionnelles." Theoretical Computer Science 123, no. 1 (1994): 131–37. http://dx.doi.org/10.1016/0304-3975(94)90073-6.

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2

Tuffin, Bruno, and Louis-Marie Le Ny. "Parallélisation d'une Combinaison des Méthodes de Monte-Carlo et Quasi-Monte-Carlo et Application aux Réseaux de Files d'Attente." RAIRO - Operations Research 34, no. 1 (2000): 85–98. http://dx.doi.org/10.1051/ro:2000106.

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3

Caflisch, Russel E. "Monte Carlo and quasi-Monte Carlo methods." Acta Numerica 7 (January 1998): 1–49. http://dx.doi.org/10.1017/s0962492900002804.

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Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N−1/2), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This article presents an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques. Accelerated convergence for Monte Carlo quadrature is attained using quasi-random (also called low-discrepancy) sequences, which are a deterministic alternative to random or pseudo-random sequences. The points in a quasi-random sequence

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4

Kleiss, Ronald, and Achilleas Lazopoulos. "Error in Monte Carlo, quasi-error in Quasi-Monte Carlo." Computer Physics Communications 175, no. 2 (2006): 93–115. http://dx.doi.org/10.1016/j.cpc.2006.02.001.

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5

Gerber, Mathieu, and Nicolas Chopin. "Sequential quasi Monte Carlo." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 77, no. 3 (2015): 509–79. http://dx.doi.org/10.1111/rssb.12104.

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6

Morokoff, William J., and Russel E. Caflisch. "Quasi-Monte Carlo Integration." Journal of Computational Physics 122, no. 2 (1995): 218–30. http://dx.doi.org/10.1006/jcph.1995.1209.

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7

Soboĺ, I. M. "Quasi-Monte Carlo methods." Progress in Nuclear Energy 24, no. 1-3 (1990): 55–61. http://dx.doi.org/10.1016/0149-1970(90)90022-w.

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8

Ziegel, Eric R., H. Niederreiter, and P. Shiue. "Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing." Technometrics 38, no. 4 (1996): 414. http://dx.doi.org/10.2307/1271337.

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9

Sobol, I. M. "On quasi-Monte Carlo integrations." Mathematics and Computers in Simulation 47, no. 2-5 (1998): 103–12. http://dx.doi.org/10.1016/s0378-4754(98)00096-2.

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10

Siyamah, Imroatus, Endah RM Putri, and Chairul Imron. "Cat bond valuation using Monte Carlo and quasi Monte Carlo method." Journal of Physics: Conference Series 1821, no. 1 (2021): 012053. http://dx.doi.org/10.1088/1742-6596/1821/1/012053.

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11

Giles, Mike, Frances Y. Kuo, Ian H. Sloan, and Benjamin J. Waterhouse. "Quasi-Monte Carlo for finance applications." ANZIAM Journal 50 (November 12, 2008): 308. http://dx.doi.org/10.21914/anziamj.v50i0.1440.

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12

Owen, A. B., and S. D. Tribble. "A quasi-Monte Carlo Metropolis algorithm." Proceedings of the National Academy of Sciences 102, no. 25 (2005): 8844–49. http://dx.doi.org/10.1073/pnas.0409596102.

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13

Hickernell, Fred J., Christiane Lemieux, and Art B. Owen. "Control Variates for Quasi-Monte Carlo." Statistical Science 20, no. 1 (2005): 1–31. http://dx.doi.org/10.1214/088342304000000468.

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14

Lécot, Christian, and Faysal El Khettabi. "Quasi-Monte Carlo Simulation of Diffusion." Journal of Complexity 15, no. 3 (1999): 342–59. http://dx.doi.org/10.1006/jcom.1999.0509.

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15

Cufaro Petroni, Nicola, and Piergiacomo Sabino. "Multidimensional quasi-Monte Carlo Malliavin Greeks." Decisions in Economics and Finance 36, no. 2 (2011): 199–224. http://dx.doi.org/10.1007/s10203-011-0125-z.

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16

Kleiss, Ronald. "Quasi-Monte Carlo, quasi-random numbers and quasi-error estimates." International Journal of Modern Physics C 04, no. 02 (1993): 323–30. http://dx.doi.org/10.1142/s0129183193000343.

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We discuss quasi-random number sequences as a basis for numerical integration with potentially better convergence properties than standard Monte Carlo. The importance of the discrepancy as both a measure of smoothness of distribution and an ingredient in the error estimate is reviewed. It is argued that the classical Koksma-Hlawka inequality is not relevant for error estimates in realistic cases, and a new class of error estimates is presented, based on a generalization of the Woźniakowski lemma.

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17

NIEDERREITER, HARALD. "QUASI-MONTE CARLO METHODS IN COMPUTATIONAL FINANCE." COSMOS 01, no. 01 (2005): 113–25. http://dx.doi.org/10.1142/s0219607705000097.

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Quasi-Monte Carlo methods are deterministic versions of Monte Carlo methods, in the sense that the random samples used in the implementation of a Monte Carlo method are replaced by judiciously chosen deterministic points with good distribution properties. They outperform classical Monte Carlo methods in many problems of scientific computing. This paper discusses applications of quasi-Monte Carlo methods to computational finance, with a special emphasis on the problems of pricing mortgage-backed securities and options. The necessary background on Monte Carlo and quasi-Monte Carlo methods is als

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18

Jank, Wolfgang. "Quasi-Monte Carlo sampling to improve the efficiency of Monte Carlo EM." Computational Statistics & Data Analysis 48, no. 4 (2005): 685–701. http://dx.doi.org/10.1016/j.csda.2004.03.019.

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19

ASTUTI, PUTU WIDYA, KOMANG DHARMAWAN, and KARTIKA SARI. "MENENTUKAN HARGA OPSI DENGAN METODE MONTE CARLO BERSYARAT MENGGUNAKAN BARISAN KUASI ACAK FAURE." E-Jurnal Matematika 10, no. 3 (2021): 141. http://dx.doi.org/10.24843/mtk.2021.v10.i03.p334.

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An option contract is a contract that gives the owner the right to sell or even to buy an asset at the predetermined price and period time. The conditional Monte Carlo is one of the several methods that is used to determine the option price which in the process uses random numbers with normal standard distribution. At the same time, the random number generator can be substituted by using a quasi-random sequence, as in Faure's quasi-random sequence. The aim of this study is to determine the contract price of the call option with the European type by applying the conditional Monte Carlo method.

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20

Biester, Christian, Peter J. Grabner, Gerhard Larcher, and Robert F. Tichy. "Adaptive Search in Quasi-Monte-Carlo Optimization." Mathematics of Computation 64, no. 210 (1995): 807. http://dx.doi.org/10.2307/2153452.

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21

Lécot, Christian, Pierre L’Ecuyer, Rami El Haddad, and Ali Tarhini. "Quasi-Monte Carlo simulation of coagulation–fragmentation." Mathematics and Computers in Simulation 161 (July 2019): 113–24. http://dx.doi.org/10.1016/j.matcom.2019.02.003.

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22

HOU, Dai-Wen, Fu-Liang YIN, and Zhe CHEN. "Quasi-Monte Carlo Filtering for Speaker Tracking." Acta Automatica Sinica 35, no. 7 (2009): 1016–21. http://dx.doi.org/10.3724/sp.j.1004.2009.01016.

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23

Snyder, William C. "Accuracy estimation for quasi-Monte Carlo simulations." Mathematics and Computers in Simulation 54, no. 1-3 (2000): 131–43. http://dx.doi.org/10.1016/s0378-4754(00)00204-4.

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24

Gribel, C. J., and T. Akenine-Möller. "Time-Continuous Quasi-Monte Carlo Ray Tracing." Computer Graphics Forum 36, no. 6 (2016): 354–67. http://dx.doi.org/10.1111/cgf.12985.

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25

L'Ecuyer, Pierre, Valérie Demers, and Bruno Tuffin. "Rare events, splitting, and quasi-Monte Carlo." ACM Transactions on Modeling and Computer Simulation 17, no. 2 (2007): 9. http://dx.doi.org/10.1145/1225275.1225280.

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26

Biester, Christian, Peter J. Grabner, Gerhard Larcher, and Robert F. Tichy. "Adaptive search in quasi-Monte Carlo optimization." Mathematics of Computation 64, no. 210 (1995): 807. http://dx.doi.org/10.1090/s0025-5718-1995-1270614-4.

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27

Joy, Corwin, Phelim P. Boyle, and Ken Seng Tan. "Quasi-Monte Carlo Methods in Numerical Finance." Management Science 42, no. 6 (1996): 926–38. http://dx.doi.org/10.1287/mnsc.42.6.926.

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28

Tian, Xiang, and Khaled Benkrid. "High-Performance Quasi-Monte Carlo Financial Simulation." ACM Transactions on Reconfigurable Technology and Systems 3, no. 4 (2010): 1–22. http://dx.doi.org/10.1145/1862648.1862656.

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29

Dick, Josef, Aicke Hinrichs, and Friedrich Pillichshammer. "Proof techniques in quasi-Monte Carlo theory." Journal of Complexity 31, no. 3 (2015): 327–71. http://dx.doi.org/10.1016/j.jco.2014.09.003.

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30

Nakano, Yumiharu. "Quasi-Monte Carlo methods for Choquet integrals." Journal of Computational and Applied Mathematics 287 (October 2015): 63–66. http://dx.doi.org/10.1016/j.cam.2015.03.026.

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31

Schlier, Ch. "Error trends in Quasi-Monte Carlo integration." Computer Physics Communications 159, no. 2 (2004): 93–105. http://dx.doi.org/10.1016/j.cpc.2004.02.004.

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32

Ben Abdellah, Amal, Pierre L'Ecuyer, Art B. Owen, and Florian Puchhammer. "Density Estimation by Randomized Quasi-Monte Carlo." SIAM/ASA Journal on Uncertainty Quantification 9, no. 1 (2021): 280–301. http://dx.doi.org/10.1137/19m1259213.

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33

Makarova, K. V., A. G. Makarov, M. A. Padalko, V. S. Strongin, and K. V. Nefedev. "Multispin Monte Carlo Method." Dal'nevostochnyi Matematicheskii Zhurnal 20, no. 2 (2020): 212–20. http://dx.doi.org/10.47910/femj202020.

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The article offers a Monte Carlo cluster method for numerically calculating a statistical sample of the state space of vector models. The statistical equivalence of subsystems in the Ising model and quasi-Markov random walks can be used to increase the efficiency of the algorithm for calculating thermodynamic means. The cluster multispin approach extends the computational capabilities of the Metropolis algorithm and allows one to find configurations of the ground and low-energy states.

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34

RATNASARI, DEWA AYU AGUNG PUTRI, KOMANG DHARMAWAN, and DESAK PUTU EKA NILAKUSMAWATI. "PENENTUAN NILAI KONTRAK OPSI TIPE BINARY PADA KOMODITS KAKAO MENGGUNAKAN METODE QUASI MONTE CARLO DENGAN BARISAN BILANGAN ACAK FAURE." E-Jurnal Matematika 6, no. 4 (2017): 214. http://dx.doi.org/10.24843/mtk.2017.v06.i04.p168.

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Contract options are the most important part of an investment strategy. An option is a contract that entitles the owner or holder to sell an asset on a designated maturity date. A binary or asset-or-nothing option is an option in which the option holder will perform or not the option. There are many methods used in determining the option contract value, one of this is the Monte Carlo Quasi method of the Faure random. The purpose of this study is to determine the value of binary type option contract using the Quasi Monte Carlo method of the Faure random and compare with the Monte Carlo method.

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35

Gurov, Todor, Aneta Karaivanova, and Vassil Alexandrov. "Energy Study of Monte Carlo and Quasi-Monte Carlo Algorithms for Solving Integral Equations." Procedia Computer Science 80 (2016): 1897–905. http://dx.doi.org/10.1016/j.procs.2016.05.492.

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36

Marques, Ricardo, Christian Bouville, Luís Paulo Santos, and Kadi Bouatouch. "Efficient Quadrature Rules for Illumination Integrals: From Quasi Monte Carlo to Bayesian Monte Carlo." Synthesis Lectures on Computer Graphics and Animation 7, no. 2 (2015): 1–92. http://dx.doi.org/10.2200/s00649ed1v01y201505cgr019.

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37

Avramidis, Athanassios N., and Pierre L’Ecuyer. "Efficient Monte Carlo and Quasi–Monte Carlo Option Pricing Under the Variance Gamma Model." Management Science 52, no. 12 (2006): 1930–44. http://dx.doi.org/10.1287/mnsc.1060.0575.

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38

Entacher, Karl, Thomas Schell, Wolfgang Ch Schmid, and Andreas Uhl. "Defects in parallel Monte Carlo and quasi-Monte Carlo integration using the leap-frog technique." Parallel Algorithms and Applications 18, no. 1-2 (2003): 13–26. http://dx.doi.org/10.1080/1063719031000088021.

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39

Hossen, SM Arif, and ABM Shahadat Hossain. "A Comparative Analysis of Monte Carlo and Quasi-Monte Carlo Methods in Financial Derivative Pricing." Dhaka University Journal of Science 69, no. 1 (2021): 1–6. http://dx.doi.org/10.3329/dujs.v69i1.54617.

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The main purpose of this dissertation is to study Monte Carlo (MC) and Quasi-Monte Carlo (QMC) methods for pricing financial derivatives. We estimate the Price of European as well as various path dependent options like Asian, Barrier and American options by using these methods. We also compute the numerical results by the above mentioned methods and compare them graphically as well with the help of the MATLAB Coding. Dhaka Univ. J. Sci. 69(1): 1-6, 2021 (January)

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40

Gerber, Mathieu, and Nicolas Chopin. "Convergence of sequential quasi-Monte Carlo smoothing algorithms." Bernoulli 23, no. 4B (2017): 2951–87. http://dx.doi.org/10.3150/16-bej834.

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41

Papageorgiou, A. "Sufficient conditions for fast quasi-Monte Carlo convergence." Journal of Complexity 19, no. 3 (2003): 332–51. http://dx.doi.org/10.1016/s0885-064x(02)00004-3.

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42

Wang, Xiaoqun, and Kai-Tai Fang. "The effective dimension and quasi-Monte Carlo integration." Journal of Complexity 19, no. 2 (2003): 101–24. http://dx.doi.org/10.1016/s0885-064x(03)00003-7.

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43

Niederreiter, Harald. "Some current issues in quasi-Monte Carlo methods." Journal of Complexity 19, no. 3 (2003): 428–33. http://dx.doi.org/10.1016/s0885-064x(03)00015-3.

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44

Baldeaux, Jan. "Quasi-Monte Carlo for finance beyond Black--Scholes." ANZIAM Journal 50 (May 27, 2009): 884. http://dx.doi.org/10.21914/anziamj.v50i0.1407.

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45

Collings, Bruce Jay, and Harald Niederreiter. "Random Number Generation and Quasi-Monte Carlo Methods." Journal of the American Statistical Association 88, no. 422 (1993): 699. http://dx.doi.org/10.2307/2290359.

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46

Ökten, Giray, and Warren Eastman. "Randomized quasi-Monte Carlo methods in pricing securities." Journal of Economic Dynamics and Control 28, no. 12 (2004): 2399–426. http://dx.doi.org/10.1016/j.jedc.2003.11.003.

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47

Ökten, G. "Error reduction techniques in quasi-monte carlo integration." Mathematical and Computer Modelling 30, no. 7-8 (1999): 61–69. http://dx.doi.org/10.1016/s0895-7177(99)00164-8.

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48

Ökten, Giray, and Matthew Willyard. "Parameterization based on randomized quasi-Monte Carlo methods." Parallel Computing 36, no. 7 (2010): 415–22. http://dx.doi.org/10.1016/j.parco.2010.03.003.

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49

Pollock, Murray, Paul Fearnhead, Adam M. Johansen, and Gareth O. Roberts. "Quasi‐stationary Monte Carlo and the ScaLE algorithm." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 82, no. 5 (2020): 1167–221. http://dx.doi.org/10.1111/rssb.12365.

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50

Dong Guo and Xiaodong Wang. "Quasi-Monte Carlo filtering in nonlinear dynamic systems." IEEE Transactions on Signal Processing 54, no. 6 (2006): 2087–98. http://dx.doi.org/10.1109/tsp.2006.873585.

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