Robust optimal strategies for an insurer with reinsurance and investment under benchmark and mean-variance criteria
Robust optimal strategies for an insurer with reinsurance and investment under benchmark and mean-variance criteria
复制标题
DOI：
10.1080/03461238.2014.883085
复制
发表时间：
2015-11
影响因子：
1.8
通讯作者：
Bo Yi;F. Viens;Zhongfei Li;Yan Zeng
中科院分区：
文献类型：
--
作者：
Bo Yi;F. Viens;Zhongfei Li;Yan Zeng
在本文中，模糊厌恶保险公司（AAI）的盈余过程近似为布朗运动漂移，希望通过投资于Black-Scholes金融市场和转移一些风险给再保险公司的风险管理，但担心模型参数的不确定性。她选择寻找投资和再保险策略，这些策略对于这种不确定性是稳健的，并在均值-方差框架中优化她的决策。利用随机动态规划方法，在粘性解的意义下，得到了鲁棒最优基准策略及其相应值函数的封闭表达式，从而得到了均值-方差有效策略和有效前沿.最后通过算例分析了其经济意义。特别是，我们在均值-方差框架中的结论在性质上不同，对于某些参数范围，在效用函数框架中的模型不确定性鲁棒性结论：模型不确定性并不总是导致代理决定在均值-方差标准下减少风险暴露，与Maenhout和Liu的效用函数结论相反。我们的结论可以解释为，AAI的均值-方差问题解释了某些违反直觉的投资者行为，对于面临模型不确定性的AAI，对风险暴露的态度取决于积极的过去经验。
In this paper, an ambiguity-averse insurer (AAI) whose surplus process is approximated by a Brownian motion with drift, hopes to manage risk by both investing in a Black–Scholes financial market and transferring some risk to a reinsurer, but worries about uncertainty in model parameters. She chooses to find investment and reinsurance strategies that are robust with respect to this uncertainty, and to optimize her decisions in a mean-variance framework. By the stochastic dynamic programming approach, we derive closed-form expressions for a robust optimal benchmark strategy and its corresponding value function, in the sense of viscosity solutions, which allows us to find a mean-variance efficient strategy and the efficient frontier. Furthermore, economic implications are analyzed via numerical examples. In particular, our conclusion in the mean-variance framework differs qualitatively, for certain parameter ranges, with model-uncertainty robustness conclusions in the framework of utility functions: model uncertainty does not always result in an agent deciding to reduce risk exposure under mean-variance criteria, opposite to the conclusions for utility functions in Maenhout and Liu. Our conclusion can be interpreted as saying that the mean-variance problem for the AAI explains certain counter-intuitive investor behaviors, by which the attitude to risk exposure, for an AAI facing model uncertainty, depends on positive past experience.