Determining the Insurer’s Optimal Investment and Reinsurance Strategy Based on Stochastic Differential Game

21 Pages Posted: 19 Jul 2011 Last revised: 30 Apr 2015

See all articles by Hong Mao

Hong Mao

Shanghai Second Polytechnic University

James M. Carson

University of Georgia

Krzysztof Ostaszewski

Illinois State University

luo yan loyal

Nanjing University

Yuling Wang

Shanghai University of Finance and Economics

Date Written: February 14, 2014

Abstract

In this paper, we discuss how to determine the optimal investment portfolio and reinsurance strategy of insurance company based on zero-sum stochastic differential game between the market and the insurer. We extend Zhang and Siu (2009)’s model by (1) including a risk-free asset, (2) considering risky assets instead of only one risky asset and (3) discussing the case of power utility function besides exponential utility when the wealth process of an insurance company is a diffusion process. We establish the Hamilton-Jacobi-Bellman-Issacs equations and obtain the optimal solutions of the amount invested in risky assets and retention of reinsurance. Our results show that the optimal solution is positively correlated to time but independent of the wealth of insurer, when the utility function of terminal wealth is exponential. However, the optimal solution is uncorrelated to time and is increasing function of the wealth of the insurer in the case of power utility function. Our results also show that the risk-free interest rate will affect the strategy of investment and reinsurance.

Suggested Citation

Mao, Hong and Carson, James M. and Ostaszewski, Krzysztof and loyal, luo yan and Wang, Yuling, Determining the Insurer’s Optimal Investment and Reinsurance Strategy Based on Stochastic Differential Game (February 14, 2014). Available at SSRN: https://ssrn.com/abstract=1888015 or http://dx.doi.org/10.2139/ssrn.1888015

Hong Mao (Contact Author)

Shanghai Second Polytechnic University ( email )

No.2360, Jinhai Road
Shanghai, 201209
China

James M. Carson

University of Georgia ( email )

Athens, GA 30602-6254
United States

Krzysztof Ostaszewski

Illinois State University ( email )

Department of Mathematics
Normal, IL 61790-4520
United States
+1-309-438-7226 (Phone)
+1-309-438-5866 (Fax)

HOME PAGE: http://math.illinoisstate.edu/krzysio

Luo yan Loyal

Nanjing University ( email )

Nanjing, Jiangsu 210093
China

Yuling Wang

Shanghai University of Finance and Economics ( email )

777 Guoding Road
Shanghai, AK Shanghai 200433
China

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