Asymptotic solution of optimal reinsurance and investment problem with correlation risk for an insurer under the CEV model

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.

Download Full-text

Optimal reinsurance and investment problem in a defaultable market

Communication in Statistics- Theory and Methods ◽

10.1080/03610926.2017.1321772 ◽

2017 ◽

Vol 47 (7) ◽

pp. 1597-1614 ◽

Cited By ~ 2

Author(s):

Jianjing Ma ◽

Guojing Wang ◽

George Xianzhi Yuan

Keyword(s):

Optimal Reinsurance ◽

Investment Problem

Download Full-text

Optimal Reinsurance-Investment Problem under Mean-Variance Criterion with n Risky Assets

Discrete Dynamics in Nature and Society ◽

10.1155/2020/6489532 ◽

2020 ◽

Vol 2020 ◽

pp. 1-16

Author(s):

Peng Yang

Keyword(s):

Financial Market ◽

Investment Strategy ◽

Hjb Equation ◽

Model Parameters ◽

Optimal Reinsurance ◽

Risky Assets ◽

Terminal Wealth ◽

Investment Problem ◽

Mean Variance ◽

Variance Criterion

Based on the mean-variance criterion, this paper investigates the continuous-time reinsurance and investment problem. The insurer’s surplus process is assumed to follow Cramér–Lundberg model. The insurer is allowed to purchase reinsurance for reducing claim risk. The reinsurance pattern that the insurer adopts is combining proportional and excess of loss reinsurance. In addition, the insurer can invest in financial market to increase his wealth. The financial market consists of one risk-free asset and n correlated risky assets. The objective is to minimize the variance of the terminal wealth under the given expected value of the terminal wealth. By applying the principle of dynamic programming, we establish a Hamilton–Jacobi–Bellman (HJB) equation. Furthermore, we derive the explicit solutions for the optimal reinsurance-investment strategy and the corresponding efficient frontier by solving the HJB equation. Finally, numerical examples are provided to illustrate how the optimal reinsurance-investment strategy changes with model parameters.

Download Full-text