Paper Info
Title
A class of non-zero-sum stochastic differential investment and reinsurance games.
Abstract
In this article, we provide a systematic study on the non-zero-sum stochastic differential investment and reinsurance game between two insurance companies. Each insurance company’s surplus process consists of a proportional reinsurance protection and an investment in risky and risk-free assets. Each insurance company is assumed to maximize his utility of the difference between his terminal surplus and that of his competitor. The surplus process of each insurance company is modeled by a mixed regime-switching Cramer–Lundberg diffusion approximation process, i.e. the coefficients of the diffusion risk processes are modulated by a continuous-time Markov chain and an independent market-index process. Correlation between the two surplus processes, independent of the risky asset process, is allowed. Despite the complex structure, we manage to solve the resulting non-zero sum game problem by applying the dynamic programming principle. The Nash equilibrium, the optimal reinsurance/investment, and the resulting value processes of the insurance companies are obtained in closed forms, together with sound economic interpretations, for the case of an exponential utility function.
Year
DOI
Venue
2014
10.1016/j.automatica.2014.05.033
Automatica
Keywords
Field
DocType
Hamiltonian–Jacobi–Bellman equation,Non-zero-sum stochastic differential game,Equilibrium investment,Equilibrium proportional reinsurance,Regime switching,Relative performance,Cramer–Lundberg model,Nash equilibrium,Stochastic control
Dynamic programming,Reinsurance,Mathematical economics,Markov chain,Zero-sum game,Exponential utility,Nash equilibrium,Mathematics,Stochastic control,Heavy traffic approximation
Journal
Volume
Issue
ISSN
50
8
0005-1098
Citations 
PageRank 
References 
4
0.43
6
Authors
4
Name
Order
Citations
PageRank
Alain Bensoussan1367170.17
Chi Chung Siu261.21
Sheung Chi Phillip Yam3335.94
Hailiang Yang440.77