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
摘要: 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。
Abstract: 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.
文章引用：刘月. 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[J]. 应用数学进展, 2023, 12(3): 860-872. https://doi.org/10.12677/AAM.2023.123088

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