A Convergent Algorithm Based on Deterministic Approximation for a Large Class of Regime-Switching Generalized Stochastic Game-Theoretic Riccati Differential Equations

TL;DR

This paper introduces a new iterative algorithm that decomposes complex regime-switching stochastic Riccati equations into deterministic subproblems, ensuring convergence and stability, and is the first of its kind for this class of equations.

Contribution

The paper develops the first general computational method for solving regime-switching stochastic game-theoretic Riccati differential equations using a deterministic approximation approach.

Findings

Algorithm converges reliably for a broad class of problems.

Numerical experiments confirm effectiveness and stability.

Method outperforms existing approaches in computational efficiency.

Abstract

This paper proposes a novel iterative algorithm to compute the stabilizing solution of regime-switching stochastic game-theoretic Riccati differential equations with periodic coefficients. The method decomposes the original complex stochastic problem into a sequence of deterministic subproblems. By sequentially solving for the minimal solutions of the Riccati differential equations in each subproblem, a sequence of matrix-valued functions is constructed. Leveraging the comparison theorem, the monotonicity, boundedness, and convergence of the iterative sequence are rigorously proven. Numerical experiments verifies algorithm effectiveness and stability. To the best of our knowledge, this is the first general computational approach developed for this class of problems.