对偶模型中带指数或线性罚函数的最优分红问题
OPTIMAL DIVIDENDS WITH EXPONENTIAL AND LINEAR PENALTY PAYMENTS IN A DUAL MODEL

本文研究了带罚函数的对偶模型的最优分红问题.假设当公司的盈余资金为负值时，公司不会发生破产，但是会进行相应的惩罚，惩罚金额取决于公司的余额水平.利用随机最优控制方法和动态规划原则，得到了最优化问题的HJB方程及其验证定理.最后，当收益服从指数分布时，得到了带指数罚函数和带线性罚函数两种情形各自的最优分红策略及最优值函数的解析式.
In this paper, we consider the optimal dividend problem with penalty payments in a dual model. We assume that the company doesn't go bankrupt when the surplus becomes negative, but penalty payments occur, and the penalty amounts are dependent on the level of the surplus. By using the stochastic optimal control approach and dynamic programming principles, we obtain the HJB equation and verification theorem for the optimal problem. Finally, when the profits follow an exponential distribution, we obtain the optimal dividend strategies and explicit solutions for exponential and linear penalty payments, respectively