Approximation of a class of non-zero-sum investment and reinsurance games for regime-switching jump–diffusion models. (May 2019)

• Record Type: Journal Article
• Authors: Bui, Trang; Cheng, Xiang; Jin, Zhuo; Yin, George
• Is Part Of: Nonlinear analysis. Volume 32(2019)
• Page Start: 276
• Page End: 293
• Publication Date: 2019-05
• Subjects: Stochastic control -- Non-zero-sum game -- Investment -- Reinsurance -- Regime switching; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2019.01.002
• Languages: English
• ISSNs: 1751-570X

Abstract

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 approximation to the Nash equilibrium by adopting the Markov chain approximation methodology. 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.