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对于一个金融或保险公司而言,寻求最优分红策略和最优分红值函数是一个受到广泛讨论的热点问题.在本文中,我们假设公司面临两类风险:Brownian风险和Poisson风险.公司可以控制其对股东的分红数额和分红时间.为了充分考虑公司经营的安全性,文中定义破产时间为公司盈余水平首次低于线性门槛b+κt的时刻,而非首次低于0的时刻,参见文献[1].本文解决了最大化公司从开始运营直至破产期间总分红折现值的期望的问题.通过求解一个含有二阶微分-积分算子的HJB方程,本文刻画出来了最优的分红值函数和最优的分红策略.结果表明,最优分红策略为线性门槛分红策略.即,当公司的盈余水平低于某线性门槛x_0+κt时,公司不分红;而当公司的盈余水平超过该线性门槛时,超过部分将全部作为红利分出.
For a financial or insurance company, finding the optimal dividend strategy and the optimal dividend value function is a hot issue that has been widely discussed. In this paper, we assume that the firm faces two types of risks: Brownian risk and Poisson risk. Companies can control In order to fully consider the safety of the company’s operation, the article defines the bankruptcy time as the moment when the company’s earnings level is below the linear threshold b + κt for the first time, rather than the moment when it is lower than 0 for the first time, see [ 1] .This paper solves the problem of maximizing the company’s expectation of discounting the total dividend from its inception until bankruptcy.By solving a HJB equation with second-order differential-integral operators, this paper depicts the optimal dividend value function And the optimal dividend strategy.The results show that the optimal dividend strategy is a linear threshold dividend strategy, that is, the company does not dividend when the company’s earnings level is below a certain linear threshold x_0 + κt, and when the company’s earnings exceed the linearity Threshold, the excess will be all part of dividends.