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| 摘要: |
| The optimal dividend strategy goes back to a paper that Bruno De Finetti presented to the International Congress of Actuaries in New York (1957). For a stock company with debit interest and dividend payments, what is the optimal strategy that maximizes the expectation of the discounted dividends until possible absolute ruin? In this paper, first, a rule for choosing the strategy that maximizes the expected accumulated discounted dividends until absolute ruin is given. Second, under the so called threshold strategy, we derive integro-differential equations for the expected accumulated discounted dividends until absolute ruin. Third, explicit expressions for the expected accumulated discounted dividends until absolute ruin with exponential claim amounts are presented. Finally, based on the explicit expressions, we show that the optimal strategy is a threshold strategy and the optimal level of threshold is also obtained. |
| 关键词: 借贷利率, 门槛分红策略, 最优策略, 期望折扣惩罚函数 |
| DOI： |
| 分类号:O211.4 |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目）, |
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| OPTIMAL DIVIDEND STRATEGIES FOR THE COMPOUND POISSON MODEL WITH DEBIT INTEREST |
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LUOKUI,XIAO Liqun
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| Abstract: |
| 最优分红策略问题可追溯到1957年在纽约举行的国际精算学大会上Bruno De Finetti的文章. 本文在允许保险公司可以借贷的情况下, 以分红总现值最大化为准则, 探讨怎样的分红策略才是最优的分红策略？我们先给出满足使分红总现值最大化的分红策略, 然后针对门槛分红策略给出分红总现值满足的微积分方程, 再在指数索赔分布下算出分红总现值的精确表达式, 最后证明门槛分红策略是最优的分红策略, 并给出最优的分红起始值。 |
| Key words: debit interest, threshold dividend strategy,optimal strategy,the expected discounted penalty function |
