Optimal investment and premium policies with ambiguity aversion

LIU Bing, ZHOU Ming

Systems Engineering - Theory & Practice ›› 2020, Vol. 40 ›› Issue (7) : 1707-1720.

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Systems Engineering - Theory & Practice ›› 2020, Vol. 40 ›› Issue (7) : 1707-1720. DOI: 10.12011/1000-6788-2019-0365-14

Optimal investment and premium policies with ambiguity aversion

  • LIU Bing1, ZHOU Ming2
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Abstract

It is of great importance to consider the investment policies and premium collections for insurers. Because of the complexity and risky of the financial market, the model of the financial market may prone to ambiguity. Hence, it is more realistic to investigate the optimal investment and premium control for insurers with consideration of the existence of ambiguity in the financial market. Intuitively, the insurance company will consider the ambiguity only exists in the financial market, while the surplus process of the insurance company will be considered completely correct due to its long-time applying, operating and testing. Under the assumption of above, the closed-form expressions for the optimal investment policy, the optimal premium control policy and the value function are obtained with maximizing the expected utility of the terminal company's wealth and with ambiguity aversion. It is concluded that there is a relationship on the optimal investment policies between considering the ambiguity aversion and without considering the ambiguity for the financial market. And the impacts of the ambiguity on optimal policies are significant.

Key words

ambiguity aversion / optimal investment policy / premium control / relative entropy / CARA (constant absolute risk aversion) utility function / HJB (Hamilton-Jacobi-Bellman) equation

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LIU Bing , ZHOU Ming. Optimal investment and premium policies with ambiguity aversion. Systems Engineering - Theory & Practice, 2020, 40(7): 1707-1720 https://doi.org/10.12011/1000-6788-2019-0365-14

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Funding

National Natural Science Foundation of China (11971506, 11571388); The MOE Project of Key Research Institute of Humanities and Social Science at Universities (15JJD790036); Humanities and Social Sciences Foundation of Ministry of Education of China (19YJCZH083)
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