报告题目：Insurance portfolio and investment-consumption for individuals with an uncovered risk
报告摘要：The optimal investment-consumption and insurance problem has been extensively studied in the past decades. In general, either life insurance or property insurance is separately investigated with regard to the investment-consumption problem for individuals. In this paper, we propose a continuous-time model in which life insurance and property insurance are incorporated at the same time together with the investment-consumption problem. It is assumed that an individual is exposed to a series of accident risks which could lead to complete loss of wealth accompanied by a potential loss of life with a positive probability each time. Furthermore, in addition to these accident risks, the individual’s future lifetime is subject to natural death. The individual manages the risks through life insurance and property insurance, however, the life insurance policy only includes coverage for natural death; accidental death is excluded. The individual’s objective is to maximize their total discounted utilities, which includes consumption, bequest, and terminal wealth at retirement. They aim to achieve this goal by selecting an investment-consumption and insurance portfolio. The value function and optimal policies are explicitly derived for the constant relative risk aversion (CRRA) utility case. The results demonstrate that, under the expected value premium principle, the optimal property insurance is proportional. Moreover, optimal policies are influenced significantly by both utility preference and accidental death, and the optimal life insurance strategy can perfectly explain the demand for reverse life insurance in the absence of bequest motivation. Finally, we present some numerical analysis to display the impact of parameters on the optimal strategies.