摘要
在通货膨胀影响下,研究了一类理赔相依风险模型的,时间一致的最优策略选择问题。两种理赔的相依性通过一个共同的泊松过程来体现。为了减小风险,保险人可以进行再保险;为了增加财富,保险人可以在金融市场上进行投资。进行投资时,考虑了通货膨胀的影响,通货膨胀的影响是通过通货膨胀率对风险资产折算实现的。研究的目标是:保险人选择时间一致的最优再保险-投资策略,最大化终止时刻财富的均值,同时最小化终止时刻财富的方差。因为该问题是时间不一致的,从博弈论的视角对问题进行了求解。应用HamiltonJacobi-Bellman动态规划的方法,得到了时间一致的最优再保险-投资策略和相应值函数的显式解。最后通过数值计算,解释了一些保险市场模型参数对最优再保险策略影响,以及金融市场模型参数和通货膨胀模型参数对最优投资策略的影响。通过研究,可以指导投资者在通货膨胀的影响下进行合理投资,使自身财富最大而风险最小。
Under inflation influence, an optimal time-consistent strategy selection problem tor claims dependent risk model is studied. The two claim number processes are correlated by a common Poisson process. The insurer can purchase reinsurance for reducing claims and invest its surplus in finance market for increasing wealth. In the process of investment, the effect of inflation is taken into account, and the effect of inflation is achieved through the conversion of the risk asset to the inflation rate. The objective of the insurer is to choose an optimal time-consistent reinsurance-investment strategy so as to maximize the expected terminal surplus while minimizing the variance of the terminal surplus. Since this problem is time-inconsistent, it is studied by placing the problem within a game theoretic framework. Applying Hamihon-Jaeobi-Bellman dynamic programming approach, closed form solutions for the optimal reinsuranceinvestment strategy and the corresponding value functions are obtained. Finally, the influence of some in surance market model parameters on optimal reinsurance strategy is explained by numerical calculation, and the influence of financial market model parameters and inflation model parameters on optimal investment strategy are also given. Through this study, it can guide investors to make reasonable investment under the influence of inflation, so that their wealth is the largest and the smallest risk.
出处
《中山大学学报（自然科学版）》
CAS
CSCD
北大核心
2017年第4期28-37,共10页
Acta Scientiarum Naturalium Universitatis Sunyatseni
基金
西京学院院科研基金(XJ160144)
陕西省教育厅科研计划项目(15JK2183)
