Simulation of Mckean-Vlasov Bsdes by Wiener Chaos Expansion

被引：0

作者：

Acary-Robert, Celine ^{[1
]}

Briand, Philippe ^{[2
]}

Ghannoum, Abir ^{[2
,3
]}

Labart, Celine ^{[2
]}

机构：

[1] Univ Grenoble Alpes, Inria, CNRS, Grenoble INP,INP,LJK, Grenoble, France

[2] Univ Savoie Mt Blanc, CNRS, LAMA, F-73000 Chambery, France

[3] Univ Libanaise, LaMA Liban, Tripoli, Lebanon

来源：

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | 2025年 / 27卷 / 02期

关键词：

McKean-Vlasov backward stochastic differential equations; Wiener chaos expansion; Particle methods; MEAN-FIELD GAMES; DISCRETE-TIME APPROXIMATION; PARTICLE METHOD; ALGORITHM; CONVERGENCE; DISCRETIZATION; STABILITY; EQUATIONS; SCHEMES;

D O I：

10.1007/s11009-025-10172-8

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We present an algorithm to solve McKean-Vlasov BSDEs based on Wiener chaos expansion and Picard's iterations and study its convergence. This paper extends the results obtained by Briand and Labart (The Annal Appl Probab 24(3):1129-1171, 2014) when standard BSDEs were considered. Here we are faced with the problem of the approximation of the law of (Y, Z) in the driver, that we solve by using a particle system. In order to avoid solving a system of BSDEs, which would not be feasible in practice, we use the same particles to approximate the law of (Y, Z) and to compute Monte Carlo approximations.

引用

页数：39

共 43 条

[1] Mean-field FBSDE and optimal control [J].

Agram, Nacira ;

Choutri, Salah Eddine .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2021, 39 (02) :235-251

[2]

Alanko S, 2015, Regression-based Monte Carlo methods for solving nonlinear PDEs

[3]

Antonelli F, 2002, ANN APPL PROBAB, V12, P423

[4] Modeling tagged pedestrian motion: A mean-field type game approach [J].

Aurell, Alexander ;

Djehiche, Boualem .

TRANSPORTATION RESEARCH PART B-METHODOLOGICAL, 2019, 121 :168-183

[5] A quantization algorithm for solving multidimensional discrete-time optimal stopping problems [J].

Bally, V ;

Pagés, G .

BERNOULLI, 2003, 9 (06) :1003-1049

[6]

Bally V., 1997, Backward stochastic differential equations (Paris, 1995-1996) Pitman Research Notes in Mathematics Series, V364, P177

[7] Time discretization and Markovian iteration for coupled FBSDES [J].

Bender, Christian ;

Zhang, Jianfeng .

ANNALS OF APPLIED PROBABILITY, 2008, 18 (01) :143-177

[8] CONJUGATE CONVEX FUNCTIONS IN OPTIMAL STOCHASTIC CONTROL [J].

BISMUT, JM .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1973, 44 (02) :384-404

[9]

Bossy M., 2005, ESAIM: proceedings, V15, P18, DOI DOI 10.1051/PROC:2005019

[10] Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations [J].

Bouchard, B ;

Touzi, N .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2004, 111 (02) :175-206

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