Approximation of A Class of Non-Zero-Sum Investment and Reinsurance Games for Regime-Switching Jump-Diffusion Models

TL;DR

This paper introduces a numerical approximation method for non-zero-sum investment and reinsurance games between insurance companies within regime-switching jump-diffusion models, providing algorithms to find Nash equilibria.

Contribution

It develops a Markov chain approximation approach for solving complex nonlinear HJI equations in regime-switching jump-diffusion models, with proven convergence and practical algorithms.

Findings

Algorithms successfully compute Nash equilibria in complex models

Convergence of approximation sequences is theoretically established

Numerical examples demonstrate practical applicability

Abstract

This work develops an approximation procedure for a class of non-zero-sum stochastic differential investment and reinsurance games between two insurance companies. Both proportional reinsurance and excess-of loss reinsurance policies are considered. We develop numerical algorithms to obtain the Nash equilibrium by adopting the Markov chain approximation methodology and applying the dynamical programming principle for the nonlinear integro-differential Hamilton-Jacobi-Isaacs (HJI) equations. Furthermore, we establish the convergence of the approximation sequences and the approximation to the value functions. Numerical examples are presented to illustrate the applicability of the algorithms.