随机零和微分对策与后向随机微分方程

IF 0.3 Q4 STATISTICS & PROBABILITY

Random Operators and Stochastic Equations Pub Date : 2023-01-30 DOI:10.1515/rose-2022-2097

Khalid Oufdil

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引用次数: 0

摘要

摘要本文在一个一般情况下研究有限域中的随机零和微分对策。我们首先证明了与特定生成器（博弈的哈密顿函数）相关的BSDE具有唯一的解。然后我们将值函数刻画为证明对策鞍点存在的解。最后，在马尔可夫框架下，我们证明了值函数是相关偏微分方程的唯一粘性解。

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Stochastic zero-sum differential games and backward stochastic differential equations

Abstract In this paper, we study the stochastic zero-sum differential game in finite horizon in a general case. We first prove that the BSDE associated with a specific generator (the Hamiltonian function for the game) has a unique solution. Then we characterize the value function as that solution to prove the existence of a saddle point for the game. Finally, in the Markovian framework, we show that the value function is the unique viscosity solution for the related partial differential equation.

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来源期刊

Random Operators and Stochastic Equations STATISTICS & PROBABILITY-

CiteScore

0.60

自引率

25.00%

发文量