Stochastic Recursive Zero-sum Differential Games with Payoff Functional in BDSDEs under Model Uncertainty
DOI:
https://doi.org/10.54097/hset.v1i.490Keywords:
Stochastic recursive 0-sum differential game, Saddle point, Model uncertainty, Backward doubly stochastic differential equations, Compare theoremAbstract
In this paper, problems related to stochastic recursive 0-sum differential games under model uncertainty are studied. In this model, the cost function is defined by 
, in which 
is the solution of a family of forward and backward doubly stochastic differential equations. We deduced the existence of the saddle points for this robust problem with the selection theorem and comparison theorem of BDSDEs. The specific form of the cost function has also been given.
Downloads
References
J.M.Bismut, An introductory approach to duality in optimal stochestic control, SIAM Rev.20,1 (1978), 62-78.
E. Pardoux & S. Peng, Adapted solution of a backward stochastic differential equation, Systerms & Control Letters. 14 (1990), 55-61.
E. Pardoux & S. Peng, Backward doubly stochastic differential equations and systems of quasilinear SPDEs, Probab. Theory Related Fields. 98 (1994), 209-227.
Y.Shi & Y.Gu & Kai Liu, Comparison theorem of backward doubly stochastic differential equations and application. Stochastic Analysis and Applications. 23 (2005), 97-110.
A. Aman & M. Nzi, Reflected Backward Doubly Stochastic Differential Equations and Application. 18 (2007).
S. Hamadene & J.-P. Lepeltier, Zero-sum stochastic differential games and backward equations, Systems Control Letters. 24, 4 (1995), 259-263.
G. Wang & Z. Yu, A Pontryagin’s maximum principle for non-zero sum differential games of BSDEs with applications, IEEE Transactions on Automatic Control, 55,7 (2010), 1742-1747.
N. El Karoui & S. Peng & M. C. Quenez, Backward stochastic differential equations in finance, Athematical Finance, 7, 1 (1997), 1-71.
L. Wei & Z. Wu, Stochastic Recursive Zero-Sum Differential Game and Mixed Zero-Sum Differential Game Problem, Mathematical Problems in Engineering, 2 (2012), 1-15.
M. Hu & F. Wang, Maximum principle for stochastic recursive optimal control problem under model uncertainty, SIAM J. CONTROL OPTIM., 58, 3 (2020), 1341-1371.
V. E. Benes, Existence of optimal strategies based on specified information, for a class of stochastic decision problems., SIAM Journal on Control and Optimization,.8 (1970), 179-188.
Osmar Francisco Giuliani. Anéis quadráticos generalizados e álgebras de posto 3 , Universidade de Sao Paulo, Agencia USP de Gestao da Informacao Academica (AGUIA), 1998.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
