Optimal Reinsurance-Investment Problem under a CEV Model: Stochastic Differential Game Formulation

This paper focuses on a stochastic differential game played between two insurance companies, a big one and a small one. In our model, the basic claim process is assumed to follow a Brownian motion with drift. Both of two insurance companies purchase the reinsurance, respectively. The big company has...

Full description

Saved in:
Bibliographic Details
Published in:Mathematical problems in engineering 2020, Vol.2020 (2020), p.1-19
Main Authors: Li, Danping, Li, Cunfang, Chen, Ruiqing
Format: Article
Language:English
Subjects:
Brownian motion
Differential games
Engineering
Expected utility
Game theory
Insurance
Insurance companies
Investment strategy
Risk exposure
Volatility
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper focuses on a stochastic differential game played between two insurance companies, a big one and a small one. In our model, the basic claim process is assumed to follow a Brownian motion with drift. Both of two insurance companies purchase the reinsurance, respectively. The big company has sufficient asset to invest in the risky asset which is described by the constant elasticity of variance (CEV) model and acquire new business like acting as a reinsurance company of other insurance companies, while the small company can invest in the risk-free asset and purchase reinsurance. The game studied here is zero-sum where there is a single exponential utility. The big company is trying to maximize the expected exponential utility of the terminal wealth to keep its advantage on surplus while simultaneously the small company is trying to minimize the same quantity to reduce its disadvantage. In this paper, we describe the Nash equilibrium of the game and prove a verification theorem for the exponential utility. By solving the corresponding Fleming-Bellman-Isaacs equations, we derive the optimal reinsurance and investment strategies. Furthermore, numerical examples are presented to show our results.
ISSN:1024-123X
1563-5147
DOI:10.1155/2020/7265121