Optimal mean–variance reinsurance and investment in a jump-diffusion financial market with common shock dependence
Optimal mean–variance reinsurance and investment in a jump-diffusion financial market with common shock dependence
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DOI：
10.1007/s00186-016-0538-0
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发表时间：
2016-04
影响因子：
1.2
通讯作者：
Zhibin Liang;Junna Bi;K. Yuen;Caibin Zhang
中科院分区：
文献类型：
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作者：
Zhibin Liang;Junna Bi;K. Yuen;Caibin Zhang
本文研究了具有跳跃扩散风险资产的金融市场中的最优再保险投资问题，其中保险风险模型受复合Poisson过程调制，并且两个跳跃数过程由一个共同冲击相关。此外，我们取消了股票市场跳跃规模期望值的非负性假设，这在经济上更合理，因为在真实的金融市场中跳跃规模总是为负的。在均值-方差准则下，基于随机线性二次控制理论，导出了最优策略的显式表达式和相应的Hamilton-Jacobi-Bellman方程的粘性解的值函数。将线性二次型情形下的结果推广到原均值-方差问题，得到了有效策略和有效边界的显式解。数值算例表明了模型参数对有效前沿的影响。
In this paper, we study the optimal reinsurance-investment problems in a financial market with jump-diffusion risky asset, where the insurance risk model is modulated by a compound Poisson process, and the two jump number processes are correlated by a common shock. Moreover, we remove the assumption of nonnegativity on the expected value of the jump size in the stock market, which is more economic reasonable since the jump sizes are always negative in the real financial market. Under the criterion of mean–variance, based on the stochastic linear–quadratic control theory, we derive the explicit expressions of the optimal strategies and value function which is a viscosity solution of the corresponding Hamilton–Jacobi–Bellman equation. Furthermore, we extend the results in the linear–quadratic setting to the original mean–variance problem, and obtain the solutions of efficient strategy and efficient frontier explicitly. Some numerical examples are given to show the impact of model parameters on the efficient frontier.