具有随机观测周期的经典风险模型中最优分红和注资策略(英文)

The Optimal Dividend and Capital Injection Strategies in the Classical Risk Model with Randomized Observation Periods

本文考虑具有随机观测周期的经典风险模型中最优分红和注资策略.假设破产是被禁止的.目的是最大化分红折现总额减去资金注射折现总额的期望值.得到了HJB方程并证明了验证性定理.并在指数理赔假设下得到了最优控制策略和最优值函数.

This paper considers the optimal dividend and capital injection strategies in the classical risk model with randomized observation periods. Assume that ruin is prohibited. We aim to maximise the expected discounted dividend payments minus the expected penalised discounted capital injections. We derive the associated Hamilton-Jacobi-Bellman （HJB） equation and prove the verification theorem. The optimal control strategy and the optimal value function are obtained under the assumption that the claim sizes are exponentially distributed.