常利率古典风险模型的按比例分红问题

Proportional Dividend Problems in the Classical Risk Model with Interest

分红问题是目前保险精算研究的一个重要课题,本文利用HJB方程的方法证明了常利率古典风险模型的最优分红策略为边界策略;推导出了最优分红策略下常利率古典风险模型的期望红利总量现值所满足的积分方程;通过拉Laplace变换技巧给出了当保险公司的初始资金u大于或等于红利界线b时的期望红利总量现值的精确结果。为保险公司更合理的分配红利和掌控资金运营提供了理论依据。

Dividend problem is an important subject in insurance actuarial study. In this paper, by using the HJB equation method, we prove that, for the classical risk model, with the regular rate, the optimal dividend strategy is the border strategy. Under the optimal dividend strategy, we derive the integral equation that the total present value of dividends of the regular rate risk model should satisfy. Basing on the Laplace transformation, the accurate total present value of dividends is obtained when the initial investment of the insurance company is greater than or equal to the dividend bound. Our results provide theoretical foundation for the reasonable allocation and control of dividend in practice.