An Optimal Feedback Control-Strategy Pair For Zero-Sum Linear-Quadratic Stochastic Differential Game: the Riccati Equation Approach

Abstract

In this paper, we study a two-person zero-sum linear-quadratic stochastic differential game problem. From a new viewpoint, we construct an optimal feedback control-strategy pair for the game in a closed-loop form based on the solution of a Riccati equation. A key part of our analysis involves proving the global solvability of this Riccati equation, which is interesting in its own right. Moreover, we demonstrate an indefinite phenomenon arising from the linear-quadratic game.

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