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arXiv · 2011.09242

Singular Perturbation of Zero-Sum Linear-Quadratic Stochastic Differential Games

Beniamin Goldys·James Yang·Zhou Zhou
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Abstract

We investigate a class of zero-sum linear-quadratic stochastic differential games on a finite time horizon governed by multiscale state equations. The multiscale nature of the problem can be leveraged to reformulate the associated generalised Riccati equation as a deterministic singular perturbation problem. In doing so, we show that, for small enough $\epsilon$, the existence of solution to the associated generalised Riccati equation is guaranteed by the existence of a solution to a decoupled pair of differential and algebraic Riccati equations with a reduced order of dimensionality. Furthermore, we are able to formulate a pair of asymptotic estimates to the value function of the game problem by constructing an approximate feedback strategy and observing the limiting value function.

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Beniamin Goldys, James Yang, Zhou Zhou. 2020-11-18. Singular Perturbation of Zero-Sum Linear-Quadratic Stochastic Differential Games. https://arxiv.org/abs/2011.09242

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