Optimal insurance contracts for a shot-noise Cox claim process and persistent insured's actions
研究了保险公司在索赔次数服从shot-noise Cox过程（受气候灾难驱动）时，如何设计最优保费、赔付额并激励投保人采取减损行动，以最大化自身期望效用，同时满足投保人的参与约束。
We consider a continuous-time model in which an insurer proposes an insurance contract to a potential insured. Motivated by climate change and catastrophic events, we assume that the number of claims process is a shot-noise Cox process. The insurer selects the premium to be paid by the potential insured and the amount to be paid for each claim. In addition, the insurer can request some actions from the potential insured to reduce the number of claims. The insurer wants to maximize his expected total utility, while the potential insured signs the contract if his expected total utility for signing the contract is greater than or equal to his expected total utility when he does not sign the contract. We obtain an analytical solution for the optimal premium, the optimal amount to be paid for each claim, and the optimal actions of the insured. This leads to interesting managerial insights.