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Optimal Reinsurance-Investment Problem under a CEV Model: Stochastic Differential Game Formulation
- Source :
- Mathematical Problems in Engineering, Vol 2020 (2020)
- Publication Year :
- 2020
- Publisher :
- Hindawi, 2020.
-
Abstract
- 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.
- Subjects :
- Reinsurance
0209 industrial biotechnology
Article Subject
Investment strategy
General Mathematics
Mathematics::Optimization and Control
02 engineering and technology
01 natural sciences
010104 statistics & probability
symbols.namesake
020901 industrial engineering & automation
Differential game
Economics
QA1-939
0101 mathematics
Brownian motion
General Engineering
Engineering (General). Civil engineering (General)
Computer Science::Computers and Society
Exponential utility
Nash equilibrium
Constant elasticity of variance model
symbols
TA1-2040
Mathematical economics
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 1024123X
- Database :
- OpenAIRE
- Journal :
- Mathematical Problems in Engineering
- Accession number :
- edsair.doi.dedup.....368d52f82461f657086bd839e78f481d
- Full Text :
- https://doi.org/10.1155/2020/7265121