Stochastic Differential Games: A Sampling Approach via FBSDEs

被引：0
作者：
Ioannis Exarchos
Evangelos Theodorou
Panagiotis Tsiotras
机构：
[1] Georgia Institute of Technology,Department of Aerospace Engineering
来源：
Dynamic Games and Applications | 2019年 / 9卷
关键词：
Stochastic differential games; Forward and backward stochastic differential equations; Numerical methods; Iterative algorithms;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The aim of this work is to present a sampling-based algorithm designed to solve various classes of stochastic differential games. The foundation of the proposed approach lies in the formulation of the game solution in terms of a decoupled pair of forward and backward stochastic differential equations (FBSDEs). In light of the nonlinear version of the Feynman–Kac lemma, probabilistic representations of solutions to the nonlinear Hamilton–Jacobi–Isaacs equations that arise for each class are obtained. These representations are in form of decoupled systems of FBSDEs, which may be solved numerically.
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页码：486 / 505
页数：19
相关论文
共 82 条
[1]  
Barles G(1991)Convergence of approximation schemes for fully nonlinear second order equations Asymptot Anal 4 271-283
[2]  
Souganidis P(1997)Galerkin approximation of the generalized Hamilton–Jacobi–Bellman equation Automatica 33 2159-2177
[3]  
Beard R(2007)A forward scheme for backward SDEs Stoch Process Appl 117 1793-1812
[4]  
Saridis G(2004)Discrete time approximation and Monte Carlo simulation of BSDEs Stoch Process Appl 111 175-206
[5]  
Wen J(2009)Discrete-time approximation of BSDEs and probabilistic schemes for fully nonlinear PDEs Radon Ser Comput Appl Math 8 91-124
[6]  
Bender C(2008)Stochastic differential games and viscosity solutions of Hamilton–Jacobi–Bellman–Isaacs equations SIAM J Control Optim 47 444-475
[7]  
Denk R(2016)Numerical simulation of quadratic BSDEs Ann Appl Probab 26 262-304
[8]  
Bouchard B(2006)Uniqueness results for second-order Bellman-Isaacs equations under quadratic growth assumptions and applications SIAM J Control Optim 45 74-106
[9]  
Touzi N(2011)On the uniqueness of solutions to quadratic BSDEs with convex generators and unbounded terminal conditions Annales de l’Institut Henri Poincarè, Probabilitès et Statistiques 47 559-574
[10]  
Bouchard B(1970)Fuel optimal reorientation of axisymmetric spacecraft J Spacecr Rockets 7 1345-1351
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