Abstract
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.
Highlights
Reinsurance is an effective way to reduce claim risk, while investment is the most common way to increase wealth.erefore, reinsurance and investment are two core problems of paramount importance in insurance and actuarial science
Browne [1] and Chen and Yang [2] studied the optimal strategy to maximize the expected exponential utility of the terminal wealth, where the surplus process is modeled by a Brownian motion with drift; Yang and Zhang [3] and Zhao et al [4] studied the optimal strategy to maximize the expected exponential utility of the terminal wealth with a jump-diffusion model; Asmussen and Taksar [5] and Chen et al [6] investigated the optimal strategy to maximize the expected value of discounted dividends paid until time of ruin; Belkina and Luo [7] and Sun [8] considered the optimal strategy to minimize the ruin probability
We considered an optimal reinsurance-investment problem under the MV criterion. e insurer’s surplus process is governed by the Cramer–Lundberg model
Summary
Reinsurance is an effective way to reduce claim risk, while investment is the most common way to increase wealth. Under the MV criterion, the optimal reinsurance-investment problem has been studied in many papers. Liang and Guo [18] considered the optimal combination of proportional and excess of loss reinsurance to maximize the expected utility. Hu et al [19] considered the problem of minimizing the probability of ruin by controlling the combination of proportional and excess of loss reinsurance. Motivated by the above-mentioned studies, this paper investigates an optimal combination of proportional and excess of loss reinsurance and investment problem under the MV criterion. (i) We first study combining proportional and excess of loss reinsurance and investment problem under the MV criterion and multiple risky assets. Liang and Guo [18] and Hu et al [19] considered the combining proportional and excess of loss reinsurance, they did not consider investment.
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