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Stochastic Differential Games: A Sampling Approach via FBSDEs

Author

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  • Ioannis Exarchos

    (Georgia Institute of Technology)

  • Evangelos Theodorou

    (Georgia Institute of Technology)

  • Panagiotis Tsiotras

    (Georgia Institute of Technology)

Abstract

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.

Suggested Citation

  • Ioannis Exarchos & Evangelos Theodorou & Panagiotis Tsiotras, 2019. "Stochastic Differential Games: A Sampling Approach via FBSDEs," Dynamic Games and Applications, Springer, vol. 9(2), pages 486-505, June.
    • Handle: RePEc:spr:dyngam:v:9:y:2019:i:2:d:10.1007_s13235-018-0268-4
    DOI: 10.1007/s13235-018-0268-4
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    References listed on IDEAS

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