A Deterministic Setting for the Numerical Computation of the Stabilizing Solutions to Stochastic Game-Theoretic Riccati Equations

In this paper, we are interested in the numerical aspects of the class of generalized Riccati difference equations which are involved in linear quadratic (LQ) stochastic difference games. More specifically, we address the problem of the numerical computation of the stabilizing solutions for this cla...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-04, Vol.11 (9), p.2068
Main Authors: Aberkane, Samir, Dragan, Vasile
Format: Article
Language:English
Subjects:
Algorithms
Computation
deterministic approach
Difference equations
Game theory
iterative computation
Iterative methods
Numerical analysis
Riccati equation
stochastic control
stochastic Riccati equations
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Summary:In this paper, we are interested in the numerical aspects of the class of generalized Riccati difference equations which are involved in linear quadratic (LQ) stochastic difference games. More specifically, we address the problem of the numerical computation of the stabilizing solutions for this class of nonlinear difference equations. We propose an iterative deterministic algorithm for the computation of such a global solution. The performances of the proposed algorithm are illustrated with some numerical examples.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11092068