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Multilevel Monte Carlo Path Simulation

Citations

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Cited by:

  1. Richard, Alexandre & Tan, Xiaolu & Yang, Fan, 2021. "Discrete-time simulation of Stochastic Volterra equations," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 109-138.
  2. Zhou, Zhengqing & Wang, Guanyang & Blanchet, Jose H. & Glynn, Peter W., 2023. "Unbiased Optimal Stopping via the MUSE," Stochastic Processes and their Applications, Elsevier, vol. 166(C).
  3. Riu Naito & Toshihiro Yamada, 2024. "Deep Kusuoka Approximation: High-Order Spatial Approximation for Solving High-Dimensional Kolmogorov Equations and Its Application to Finance," Computational Economics, Springer;Society for Computational Economics, vol. 64(3), pages 1443-1461, September.
  4. Aintablian, Sebouh & Khoury, Wissam El, 2017. "A simulation on the presence of competing bidders in mergers and acquisitions," Finance Research Letters, Elsevier, vol. 22(C), pages 233-243.
  5. Ferreiro-Castilla, A. & Kyprianou, A.E. & Scheichl, R. & Suryanarayana, G., 2014. "Multilevel Monte Carlo simulation for Lévy processes based on the Wiener–Hopf factorisation," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 985-1010.
  6. Michael B. Giles & Yuan Xia, 2017. "Multilevel Monte Carlo for exponential Lévy models," Finance and Stochastics, Springer, vol. 21(4), pages 995-1026, October.
  7. Antoine Jacquier & Emma R. Malone & Mugad Oumgari, 2019. "Stacked Monte Carlo for option pricing," Papers 1903.10795, arXiv.org.
  8. Denis Belomestny & Fabian Dickmann & Tigran Nagapetyan, 2013. "Pricing American options via multi-level approximation methods," Papers 1303.1334, arXiv.org, revised Dec 2013.
  9. Andrei Cozma & Christoph Reisinger, 2017. "Strong convergence rates for Euler approximations to a class of stochastic path-dependent volatility models," Papers 1706.07375, arXiv.org, revised Oct 2018.
  10. Aslett, Louis J.M. & Nagapetyan, Tigran & Vollmer, Sebastian J., 2017. "Multilevel Monte Carlo for Reliability Theory," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 188-196.
  11. Ahmed Kebaier & Jérôme Lelong, 2018. "Coupling Importance Sampling and Multilevel Monte Carlo using Sample Average Approximation," Post-Print hal-01214840, HAL.
  12. Lay Harold A. & Colgin Zane & Reshniak Viktor & Khaliq Abdul Q. M., 2018. "On the implementation of multilevel Monte Carlo simulation of the stochastic volatility and interest rate model using multi-GPU clusters," Monte Carlo Methods and Applications, De Gruyter, vol. 24(4), pages 309-321, December.
  13. Ajay Jasra & Kody Law & Carina Suciu, 2020. "Advanced Multilevel Monte Carlo Methods," International Statistical Review, International Statistical Institute, vol. 88(3), pages 548-579, December.
  14. Abgrall, R. & Congedo, P.M. & Geraci, G., 2017. "Towards a unified multiresolution scheme for treating discontinuities in differential equations with uncertainties," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 139(C), pages 1-22.
  15. McLeish, Don, 2011. "A general method for debiasing a Monte Carlo estimator," Monte Carlo Methods and Applications, De Gruyter, vol. 17(4), pages 301-315, December.
  16. Mohamed Mrad, 2022. "Solving some Stochastic Partial Differential Equations driven by Lévy Noise using two SDEs. ," Post-Print hal-03211171, HAL.
  17. Michael B. Giles & Lukasz Szpruch, 2012. "Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without L\'{e}vy area simulation," Papers 1202.6283, arXiv.org, revised May 2014.
  18. Peter Kloeden & Andreas Neuenkirch & Raffaella Pavani, 2011. "Multilevel Monte Carlo for stochastic differential equations with additive fractional noise," Annals of Operations Research, Springer, vol. 189(1), pages 255-276, September.
  19. Michael B. Giles & Francisco Bernal, 2017. "Multilevel estimation of expected exit times and other functionals of stopped diffusions," Papers 1710.07492, arXiv.org, revised Sep 2018.
  20. Stéphane Crépey & Noufel Frikha & Azar Louzi, 2024. "A Multilevel Stochastic Approximation Algorithm for Value-at-Risk and Expected Shortfall Estimation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-04037328, HAL.
  21. Chao Zheng & Jiangtao Pan, 2023. "Unbiased estimators for the Heston model with stochastic interest rates," Papers 2301.12072, arXiv.org, revised Aug 2023.
  22. Hideyuki Tanaka & Toshihiro Yamada, 2012. "Strong Convergence for Euler-Maruyama and Milstein Schemes with Asymptotic Method," Papers 1210.0670, arXiv.org, revised Nov 2013.
  23. Jorge González Cázares & Aleksandar Mijatović, 2022. "Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation," Finance and Stochastics, Springer, vol. 26(4), pages 671-732, October.
  24. Javier Frutos & Víctor Gatón, 2017. "Chebyshev reduced basis function applied to option valuation," Computational Management Science, Springer, vol. 14(4), pages 465-491, October.
  25. Siow Woon Jeng & Adem Kiliçman, 2021. "On Multilevel and Control Variate Monte Carlo Methods for Option Pricing under the Rough Heston Model," Mathematics, MDPI, vol. 9(22), pages 1-32, November.
  26. Yasa Syed & Guanyang Wang, 2023. "Optimal randomized multilevel Monte Carlo for repeatedly nested expectations," Papers 2301.04095, arXiv.org, revised May 2023.
  27. Devang Sinha & Siddhartha P. Chakrabarty, 2022. "Multilevel Monte Carlo and its Applications in Financial Engineering," Papers 2209.14549, arXiv.org.
  28. Nabil Kahalé, 2020. "Randomized Dimension Reduction for Monte Carlo Simulations," Management Science, INFORMS, vol. 66(3), pages 1421-1439, March.
  29. Palar, Pramudita Satria & Zuhal, Lavi Rizki & Shimoyama, Koji & Tsuchiya, Takeshi, 2018. "Global sensitivity analysis via multi-fidelity polynomial chaos expansion," Reliability Engineering and System Safety, Elsevier, vol. 170(C), pages 175-190.
  30. Andrei Cozma & Christoph Reisinger, 2015. "Exponential integrability properties of Euler discretization schemes for the Cox-Ingersoll-Ross process," Papers 1601.00919, arXiv.org.
  31. Fabian Dickmann & Nikolaus Schweizer, 2014. "Faster Comparison of Stopping Times by Nested Conditional Monte Carlo," Papers 1402.0243, arXiv.org.
  32. Benjamin Jourdain & Mohamed Sbai, 2013. "High order discretization schemes for stochastic volatility models," Post-Print hal-00409861, HAL.
  33. Michael B. Giles & Kristian Debrabant & Andreas Ro{ss}ler, 2013. "Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation," Papers 1302.4676, arXiv.org, revised Jun 2019.
  34. Imry Rosenbaum & Jeremy Staum, 2017. "Multilevel Monte Carlo Metamodeling," Operations Research, INFORMS, vol. 65(4), pages 1062-1077, August.
  35. Devang Sinha & Siddhartha P. Chakrabarty, 2022. "Multilevel Richardson-Romberg and Importance Sampling in Derivative Pricing," Papers 2209.00821, arXiv.org.
  36. Shuaiqiang Liu & Lech A. Grzelak & Cornelis W. Oosterlee, 2022. "The Seven-League Scheme: Deep Learning for Large Time Step Monte Carlo Simulations of Stochastic Differential Equations," Risks, MDPI, vol. 10(3), pages 1-27, February.
  37. Denis Belomestny & Tigran Nagapetyan, 2014. "Multilevel path simulation for weak approximation schemes," Papers 1406.2581, arXiv.org, revised Oct 2014.
  38. Stéphane Crépey & Noufel Frikha & Azar Louzi & Gilles Pagès, 2023. "Asymptotic Error Analysis of Multilevel Stochastic Approximations for the Value-at-Risk and Expected Shortfall," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-04304985, HAL.
  39. Bourgey Florian & De Marco Stefano & Gobet Emmanuel & Zhou Alexandre, 2020. "Multilevel Monte Carlo methods and lower–upper bounds in initial margin computations," Monte Carlo Methods and Applications, De Gruyter, vol. 26(2), pages 131-161, June.
  40. Zhengqing Zhou & Guanyang Wang & Jose Blanchet & Peter W. Glynn, 2021. "Unbiased Optimal Stopping via the MUSE," Papers 2106.02263, arXiv.org, revised Dec 2022.
  41. Dirk Becherer & Plamen Turkedjiev, 2014. "Multilevel approximation of backward stochastic differential equations," Papers 1412.3140, arXiv.org.
  42. Wei Fang & Zhenru Wang & Michael B. Giles & Chris H. Jackson & Nicky J. Welton & Christophe Andrieu & Howard Thom, 2022. "Multilevel and Quasi Monte Carlo Methods for the Calculation of the Expected Value of Partial Perfect Information," Medical Decision Making, , vol. 42(2), pages 168-181, February.
  43. Zheng, Xiaoyu & Tamaki, Hitoshi & Sugiyama, Tomoyuki & Maruyama, Yu, 2022. "Dynamic probabilistic risk assessment of nuclear power plants using multi-fidelity simulations," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
  44. Chiang, Nai-Yuan & Lin, Yiqing & Long, Quan, 2020. "Efficient propagation of uncertainties in manufacturing supply chains: Time buckets, L-leap, and multilevel Monte Carlo methods," Operations Research Perspectives, Elsevier, vol. 7(C).
  45. Alfonsi, Aurélien & Cherchali, Adel & Infante Acevedo, Jose Arturo, 2021. "Multilevel Monte-Carlo for computing the SCR with the standard formula and other stress tests," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 234-260.
  46. Aur'elien Alfonsi & Ahmed Kebaier, 2021. "Approximation of Stochastic Volterra Equations with kernels of completely monotone type," Papers 2102.13505, arXiv.org, revised Mar 2022.
  47. Sylvestre Burgos & M. B. Giles, 2011. "The computation of Greeks with multilevel Monte Carlo," Papers 1102.1348, arXiv.org.
  48. F Bourgey & S de Marco & Emmanuel Gobet & Alexandre Zhou, 2020. "Multilevel Monte-Carlo methods and lower-upper bounds in Initial Margin computations," Working Papers hal-02430430, HAL.
  49. Nagy Shady Ahmed & El-Beltagy Mohamed A. & Wafa Mohamed, 2020. "Multilevel Monte Carlo by using the Halton sequence," Monte Carlo Methods and Applications, De Gruyter, vol. 26(3), pages 193-203, September.
  50. Yi Chen & Jing Dong & Hao Ni, 2021. "ɛ-Strong Simulation of Fractional Brownian Motion and Related Stochastic Differential Equations," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 559-594, May.
  51. Bayer Christian & Szepessy Anders & Tempone Raúl, 2010. "Adaptive weak approximation of reflected and stopped diffusions," Monte Carlo Methods and Applications, De Gruyter, vol. 16(1), pages 1-67, January.
  52. Christian Bayer & Chiheb Ben Hammouda & Raul Tempone, 2020. "Multilevel Monte Carlo with Numerical Smoothing for Robust and Efficient Computation of Probabilities and Densities," Papers 2003.05708, arXiv.org, revised Oct 2023.
  53. Antoine Jacquier & Louis Jeannerod, 2017. "How many paths to simulate correlated Brownian motions?," Papers 1708.05352, arXiv.org.
  54. Aur'elien Alfonsi & Adel Cherchali & Jose Arturo Infante Acevedo, 2020. "Multilevel Monte-Carlo for computing the SCR with the standard formula and other stress tests," Papers 2010.12651, arXiv.org, revised Apr 2021.
  55. Kontosakos, Vasileios E. & Mendonca, Keegan & Pantelous, Athanasios A. & Zuev, Konstantin M., 2021. "Pricing discretely-monitored double barrier options with small probabilities of execution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 313-330.
  56. F Bourgey & S de Marco & Emmanuel Gobet & Alexandre Zhou, 2020. "Multilevel Monte-Carlo methods and lower-upper bounds in Initial Margin computations," Post-Print hal-02430430, HAL.
  57. Pingping Zeng & Ziqing Xu & Pingping Jiang & Yue Kuen Kwok, 2023. "Analytical solvability and exact simulation in models with affine stochastic volatility and Lévy jumps," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 842-890, July.
  58. Sergii Kuchuk-Iatsenko & Yuliya Mishura, 2016. "Option pricing in the model with stochastic volatility driven by Ornstein--Uhlenbeck process. Simulation," Papers 1601.01128, arXiv.org.
  59. Mouna Ben Derouich & Ahmed Kebaier, 2022. "Interpolated Drift Implicit Euler MLMC Method for Barrier Option Pricing and application to CIR and CEV Models," Papers 2210.00779, arXiv.org, revised Sep 2024.
  60. Adam Speight, 2010. "Multigrid Techniques in Economics," Operations Research, INFORMS, vol. 58(4-part-2), pages 1057-1078, August.
  61. Chang-han Rhee & Peter W. Glynn, 2012. "A new approach to unbiased estimation for SDE's," Papers 1207.2452, arXiv.org.
  62. Florian Bourgey & Stefano De Marco, 2021. "Multilevel Monte Carlo simulation for VIX options in the rough Bergomi model," Papers 2105.05356, arXiv.org, revised Jun 2022.
  63. Denis Belomestny & John Schoenmakers & Fabian Dickmann, 2013. "Multilevel dual approach for pricing American style derivatives," Finance and Stochastics, Springer, vol. 17(4), pages 717-742, October.
  64. Jorge Ignacio Gonz'alez C'azares & Aleksandar Mijatovi'c & Ger'onimo Uribe Bravo, 2018. "Geometrically Convergent Simulation of the Extrema of L\'{e}vy Processes," Papers 1810.11039, arXiv.org, revised Jun 2021.
  65. Ahmed Kebaier & Jérôme Lelong, 2017. "Coupling Importance Sampling and Multilevel Monte Carlo using Sample Average Approximation," Working Papers hal-01214840, HAL.
  66. Adrien Genin & Peter Tankov, 2016. "Optimal importance sampling for L\'evy Processes," Papers 1608.04621, arXiv.org.
  67. Goda, Takashi & Kitade, Wataru, 2023. "Constructing unbiased gradient estimators with finite variance for conditional stochastic optimization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 743-763.
  68. Andrei Cozma & Christoph Reisinger, 2015. "A mixed Monte Carlo and PDE variance reduction method for foreign exchange options under the Heston-CIR model," Papers 1509.01479, arXiv.org, revised Apr 2016.
  69. Ajay Jasra & Mohamed Maama & Aleksandar Mijatovi'c, 2024. "Modeling of Measurement Error in Financial Returns Data," Papers 2408.07405, arXiv.org.
  70. Cui, Zhenyu & Fu, Michael C. & Peng, Yijie & Zhu, Lingjiong, 2020. "Optimal unbiased estimation for expected cumulative discounted cost," European Journal of Operational Research, Elsevier, vol. 286(2), pages 604-618.
  71. Lokman A. Abbas-Turki & Stéphane Crépey & Babacar Diallo, 2018. "Xva Principles, Nested Monte Carlo Strategies, And Gpu Optimizations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(06), pages 1-40, September.
  72. Simonella, Roberta & Vázquez, Carlos, 2023. "XVA in a multi-currency setting with stochastic foreign exchange rates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 59-79.
  73. Giorgi Daphné & Lemaire Vincent & Pagès Gilles, 2017. "Limit theorems for weighted and regular Multilevel estimators," Monte Carlo Methods and Applications, De Gruyter, vol. 23(1), pages 43-70, March.
  74. Mike Giles & Yuan Xia, 2014. "Multilevel Monte Carlo For Exponential L\'{e}vy Models," Papers 1403.5309, arXiv.org, revised May 2017.
  75. Gilles Pagès & Clément Rey, 2023. "Discretization of the Ergodic Functional Central Limit Theorem," Journal of Theoretical Probability, Springer, vol. 36(1), pages 1-44, March.
  76. Al Gerbi, A. & Jourdain, B. & Clément, E., 2018. "Asymptotics for the normalized error of the Ninomiya–Victoir scheme," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 1889-1928.
  77. Yuan Xia, 2011. "Multilevel Monte Carlo method for jump-diffusion SDEs," Papers 1106.4730, arXiv.org.
  78. Al Gerbi Anis & Jourdain Benjamin & Clément Emmanuelle, 2016. "Ninomiya–Victoir scheme: Strong convergence, antithetic version and application to multilevel estimators," Monte Carlo Methods and Applications, De Gruyter, vol. 22(3), pages 197-228, September.
  79. Hideyuki Tanaka & Toshihiro Yamada, 2013. "Strong Convergence for Euler-Maruyama and Milstein Schemes with Asymptotic Method (Forthcoming in "International Journal of Theoretical and Applied Finance")," CARF F-Series CARF-F-333, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  80. St'ephane Cr'epey & Noufel Frikha & Azar Louzi, 2023. "A Multilevel Stochastic Approximation Algorithm for Value-at-Risk and Expected Shortfall Estimation," Papers 2304.01207, arXiv.org, revised Jul 2024.
  81. Dong An & Noah Linden & Jin-Peng Liu & Ashley Montanaro & Changpeng Shao & Jiasu Wang, 2020. "Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance," Papers 2012.06283, arXiv.org, revised Jun 2021.
  82. Weinan E & Martin Hutzenthaler & Arnulf Jentzen & Thomas Kruse, 2021. "Multilevel Picard iterations for solving smooth semilinear parabolic heat equations," Partial Differential Equations and Applications, Springer, vol. 2(6), pages 1-31, December.
  83. Aryo Sasongko & Cynthia Afriani Utama & Buddi Wibowo & Zaäfri Ananto Husodo, 2019. "Modifying Hybrid Optimisation Algorithms to Construct Spot Term Structure of Interest Rates and Proposing a Standardised Assessment," Computational Economics, Springer;Society for Computational Economics, vol. 54(3), pages 957-1003, October.
  84. Daphné Giorgi & Vincent Lemaire & Gilles Pagès, 2020. "Weak Error for Nested Multilevel Monte Carlo," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1325-1348, September.
  85. Genin, Adrien & Tankov, Peter, 2020. "Optimal importance sampling for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 20-46.
  86. Rainer Avikainen, 2009. "On irregular functionals of SDEs and the Euler scheme," Finance and Stochastics, Springer, vol. 13(3), pages 381-401, September.
  87. Michael B. Giles & Abdul-Lateef Haji-Ali, 2019. "Sub-sampling and other considerations for efficient risk estimation in large portfolios," Papers 1912.05484, arXiv.org, revised Apr 2022.
  88. Jan Baldeaux, 2011. "Exact Simulation of the 3/2 Model," Papers 1105.3297, arXiv.org, revised May 2011.
  89. Mohamed Mrad, 2021. "Solving some Stochastic Partial Differential Equations driven by Lévy Noise using two SDEs. ," Working Papers hal-03211171, HAL.
  90. Dereich, Steffen, 2021. "General multilevel adaptations for stochastic approximation algorithms II: CLTs," Stochastic Processes and their Applications, Elsevier, vol. 132(C), pages 226-260.
  91. Proppe, Carsten, 2021. "Local reliability based sensitivity analysis with the moving particles method," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
  92. Lord, Gabriel & Wang, Mengchao, 2024. "Convergence of a exponential tamed method for a general interest rate model," Applied Mathematics and Computation, Elsevier, vol. 467(C).
  93. Nabil Kahale, 2018. "General multilevel Monte Carlo methods for pricing discretely monitored Asian options," Papers 1805.09427, arXiv.org, revised Sep 2018.
  94. Roy Cerqueti & Viviana Fanelli, 2021. "Long memory and crude oil’s price predictability," Annals of Operations Research, Springer, vol. 299(1), pages 895-906, April.
  95. Gunther Leobacher, 2017. "A short introduction to quasi-Monte Carlo option pricing," Papers 1707.04293, arXiv.org, revised Jul 2017.
  96. Li, Chenxu & Wu, Linjia, 2019. "Exact simulation of the Ornstein–Uhlenbeck driven stochastic volatility model," European Journal of Operational Research, Elsevier, vol. 275(2), pages 768-779.
  97. Devang Sinha & Siddhartha P. Chakrabarty, 2024. "Multilevel Monte Carlo in Sample Average Approximation: Convergence, Complexity and Application," Papers 2407.18504, arXiv.org.
  98. Ruzayqat Hamza M. & Jasra Ajay, 2020. "Unbiased estimation of the solution to Zakai’s equation," Monte Carlo Methods and Applications, De Gruyter, vol. 26(2), pages 113-129, June.
  99. Michael B. Giles & Abdul-Lateef Haji-Ali & Jonathan Spence, 2023. "Efficient Risk Estimation for the Credit Valuation Adjustment," Papers 2301.05886, arXiv.org, revised May 2024.
  100. Andrei Cozma & Christoph Reisinger, 2017. "Strong order 1/2 convergence of full truncation Euler approximations to the Cox-Ingersoll-Ross process," Papers 1704.07321, arXiv.org, revised Oct 2018.
  101. Gerstner, Thomas & Griebel, Michael & Holtz, Markus, 2009. "Efficient deterministic numerical simulation of stochastic asset-liability management models in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 434-446, June.
  102. Michael B. Giles & Abdul-Lateef Haji-Ali, 2022. "Multilevel Path Branching for Digital Options," Papers 2209.03017, arXiv.org, revised Jun 2024.
  103. Jian Wang & Xiang Gao & Zhili Sun, 2021. "A Multilevel Simulation Method for Time-Variant Reliability Analysis," Sustainability, MDPI, vol. 13(7), pages 1-16, March.
  104. Jean-Francois Chassagneux & Antoine Jacquier & Ivo Mihaylov, 2014. "An explicit Euler scheme with strong rate of convergence for financial SDEs with non-Lipschitz coefficients," Papers 1405.3561, arXiv.org, revised Apr 2016.
  105. González, I.V. & Valdebenito, M.A. & Correa, J.I. & Jensen, H.A., 2019. "Calculation of second order statistics of uncertain linear systems applying reduced order models," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
  106. Jikai Jin & Yiping Lu & Jose Blanchet & Lexing Ying, 2022. "Minimax Optimal Kernel Operator Learning via Multilevel Training," Papers 2209.14430, arXiv.org, revised Jul 2023.
  107. Stéphane Crépey & Noufel Frikha & Azar Louzi, 2024. "A Multilevel Stochastic Approximation Algorithm for Value-at-Risk and Expected Shortfall Estimation," Working Papers hal-04037328, HAL.
  108. Abdul-Lateef Haji-Ali & Jonathan Spence, 2023. "Nested Multilevel Monte Carlo with Biased and Antithetic Sampling," Papers 2308.07835, arXiv.org.
  109. Albert Ferreiro-Castilla & Kees van Schaik, 2013. "Applying the Wiener-Hopf Monte Carlo simulation technique for Levy processes to path functionals such as first passage times, undershoots and overshoots," Papers 1306.3923, arXiv.org, revised Mar 2014.
  110. Denis Belomestny & Tigran Nagapetyan, 2014. "Variance reduced multilevel path simulation: going beyond the complexity $\varepsilon^{-2}$," Papers 1412.4045, arXiv.org, revised Mar 2017.
  111. Volk-Makarewicz, Warren & Borovkova, Svetlana & Heidergott, Bernd, 2022. "Assessing the impact of jumps in an option pricing model: A gradient estimation approach," European Journal of Operational Research, Elsevier, vol. 298(2), pages 740-751.
  112. Le Maître, O.P. & Knio, O.M., 2015. "PC analysis of stochastic differential equations driven by Wiener noise," Reliability Engineering and System Safety, Elsevier, vol. 135(C), pages 107-124.
  113. Michael Gnewuch & Jan Baldeaux, 2012. "Optimal Randomized Multilevel Algorithms for Infinite-Dimensional Integration on Function Spaces with ANOVA-Type Decomposition," Research Paper Series 313, Quantitative Finance Research Centre, University of Technology, Sydney.
  114. Philipp Doersek & Eskil Hansen, 2012. "High order splitting schemes with complex timesteps and their application in mathematical finance," Papers 1210.5392, arXiv.org.
  115. K. Bujok & B. M. Hambly & C. Reisinger, 2015. "Multilevel Simulation of Functionals of Bernoulli Random Variables with Application to Basket Credit Derivatives," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 579-604, September.
  116. Andreas Neuenkirch & Lukasz Szpruch, 2012. "First order strong approximations of scalar SDEs with values in a domain," Papers 1209.0390, arXiv.org.
  117. Nan Chen & Zhengyu Huang, 2013. "Localization and Exact Simulation of Brownian Motion-Driven Stochastic Differential Equations," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 591-616, August.
  118. Matti Vihola & Jouni Helske & Jordan Franks, 2020. "Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1339-1376, December.
  119. P. P. Osei & A. Jasra, 2018. "Estimating option prices using multilevel particle filters," Papers 1806.01734, arXiv.org.
  120. Beskos, Alexandros & Jasra, Ajay & Law, Kody & Tempone, Raul & Zhou, Yan, 2017. "Multilevel sequential Monte Carlo samplers," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1417-1440.
  121. Ahmed Kebaier & J'er^ome Lelong, 2015. "Coupling Importance Sampling and Multilevel Monte Carlo using Sample Average Approximation," Papers 1510.03590, arXiv.org, revised Jul 2017.
  122. Alaya, Mohamed Ben & Hajji, Kaouther & Kebaier, Ahmed, 2016. "Importance sampling and statistical Romberg method for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 1901-1931.
  123. Dereich, Steffen & Heidenreich, Felix, 2011. "A multilevel Monte Carlo algorithm for Lévy-driven stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1565-1587, July.
  124. Kahalé, Nabil, 2020. "General multilevel Monte Carlo methods for pricing discretely monitored Asian options," European Journal of Operational Research, Elsevier, vol. 287(2), pages 739-748.
  125. Huijie Zhu & Sheng Liu & Zhiqiang Yao & Moses Chukwuka Okonkwo & Zheng Peng, 2021. "A novel method for asynchronous source localisation based on time of arrival measurements," International Journal of Distributed Sensor Networks, , vol. 17(10), pages 15501477211, October.
  126. Jorge Gonz'alez C'azares & Aleksandar Mijatovi'c, 2020. "Simulation of the drawdown and its duration in L\'{e}vy models via stick-breaking Gaussian approximation," Papers 2011.06618, arXiv.org, revised Mar 2021.
  127. Ben Alaya Mohamed & Kebaier Ahmed, 2014. "Multilevel Monte Carlo for Asian options and limit theorems," Monte Carlo Methods and Applications, De Gruyter, vol. 20(3), pages 181-194, September.
  128. Hoel Håkon & von Schwerin Erik & Szepessy Anders & Tempone Raúl, 2014. "Implementation and analysis of an adaptive multilevel Monte Carlo algorithm," Monte Carlo Methods and Applications, De Gruyter, vol. 20(1), pages 1-41, March.
  129. Yu Li & Antony Ware, 2024. "A weighted multilevel Monte Carlo method," Papers 2405.03453, arXiv.org.
  130. Jingxu Xu & Zeyu Zheng, 2023. "Gradient-Based Simulation Optimization Algorithms via Multi-Resolution System Approximations," INFORMS Journal on Computing, INFORMS, vol. 35(3), pages 633-651, May.
  131. Klaus Schmitz Abe, 2011. "Pricing exotic options using MSL-MC," Quantitative Finance, Taylor & Francis Journals, vol. 11(9), pages 1379-1392, October.
  132. Warne, David J. & Baker, Ruth E. & Simpson, Matthew J., 2018. "Multilevel rejection sampling for approximate Bayesian computation," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 71-86.
  133. Rudiger Frey & Verena Kock, 2021. "Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematics," Papers 2109.11403, arXiv.org, revised Sep 2021.
  134. Mike Giles & Lukasz Szpruch, 2012. "Multilevel Monte Carlo methods for applications in finance," Papers 1212.1377, arXiv.org.
  135. Pierre E. Jacob & John O’Leary & Yves F. Atchadé, 2020. "Unbiased Markov chain Monte Carlo methods with couplings," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 543-600, July.
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