分红率有界下带借贷利率的经典模型的最优分红与注资问题

Optimal Dividend and Capital Injection Problems for Classical Models with Debit In-terest: The Case of Bounded Dividend Rates

本文研究了在分红率有界的情况下,带借贷利率的经典风险模型中最优分红与注资问题。目标是最大化绝对破产前的累计折现分红与注资成本之差,首先给出值函数和可行策略的性质,然后得到了动态规划原理和验证定理。

In this paper, we study the optimal dividend and capital injection problem of the classical risk model with interest rate. Our objective is to find a dividend and capital injection policy that maxim-izes the difference between the cumulative expected discounted dividend pay-outs and the cumula-tive expected discounted capital injection until the time of absolute bankruptcy. Firstly, we show the basic properties of the value function and admissible strategies. Then we get the dynamic pro-gramming principles and verification theorem.