TY - GEN
T1 - Stochastic Zero-Sum Differential Games for Forward-Backward SDEs
AU - Moon, Jun
AU - Basar, Tamer
N1 - Funding Information:
Research of Tamer Bas¸ar was supported in part by the Office of Naval Research (ONR) MURI Grant N00014-16-1-2710, and in part by a grant from the Air Force Office of Scientific Research (AFOSR) Jun Moon is with the School of Electrical and Computer Engineering, University of Seoul, Seoul 02504, South Korea; email: jmoon12@uos.ac.kr.
Funding Information:
Research of Jun Moon was supported in part by the National Research Foundation of Korea Grant funded by the Ministry of Science and ICT, Korea (NRF-2017R1E1A1A03070936, NRF-2017R1A5A1015311), and in part by Institute for Information & communications Technology Promotion grant funded by the Korea government, Korea (No. 2018-0-00958).
Publisher Copyright:
© 2019 IEEE.
PY - 2019/12
Y1 - 2019/12
N2 - We consider stochastic zero-sum differential games (SZSDGs) described by fully-coupled forward-backward stochastic differential equations (FBSDEs). The fully-coupled FBSDE means that the drift and diffusion terms of forward SDEs depend on the solution of the backward SDE (BSDE). The objective functional is modeled by the BSDE part of the FBSDE. For the lower and upper value functions of the SZSDG, we establish the dynamic programming principle via the generalized stochastic backward semigroup associated with the BSDE. We then show that the (lower and upper) value functions are viscosity solutions to the associated HamiltonJacobi-Isaacs partial differential equations together with an algebraic equation. This additional algebraic equation emerges due to dependence of the diffusion term on the solution of the BSDE. The problem formulation and the results of this paper generalize those in the existing literature on SZSDGs to the controlled FBSDE framework.
AB - We consider stochastic zero-sum differential games (SZSDGs) described by fully-coupled forward-backward stochastic differential equations (FBSDEs). The fully-coupled FBSDE means that the drift and diffusion terms of forward SDEs depend on the solution of the backward SDE (BSDE). The objective functional is modeled by the BSDE part of the FBSDE. For the lower and upper value functions of the SZSDG, we establish the dynamic programming principle via the generalized stochastic backward semigroup associated with the BSDE. We then show that the (lower and upper) value functions are viscosity solutions to the associated HamiltonJacobi-Isaacs partial differential equations together with an algebraic equation. This additional algebraic equation emerges due to dependence of the diffusion term on the solution of the BSDE. The problem formulation and the results of this paper generalize those in the existing literature on SZSDGs to the controlled FBSDE framework.
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U2 - 10.1109/CDC40024.2019.9030147
DO - 10.1109/CDC40024.2019.9030147
M3 - Conference contribution
AN - SCOPUS:85082491558
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 6350
EP - 6355
BT - 2019 IEEE 58th Conference on Decision and Control, CDC 2019
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 58th IEEE Conference on Decision and Control, CDC 2019
Y2 - 11 December 2019 through 13 December 2019
ER -