一类分红速率具有正下界限制的最优分红问题

A Probe into the Optimal Dividend Problem with a Positive Lower Bound Constraint on Dividend Rate

以保险公司的资产管理问题为背景,研究一类连续时间的最优分红问题.通过用带漂移的布朗运动刻画公司的保险盈余,用单调不减的右连续、左极限的可测过程刻画公司的分红,建立随机最优控制问题,并得到相应的HJB方程.最终分别给出两种约束下的方程解的表达式和自由边界点存在的条件.研究成果可为公司的决策提供定性定量的依据.

Based on the asset management problem of insurance companies,a class of optimal dividend problems with continuous time is studied.By using Brownian motion with drift to characterize the company's insurance surplus,and using a non decreasing,right continuous and left limit measurable process to characterize the dividends,the optimal control problem and the corresponding HJB equation can be established.In the end,the expressions of the solutions of the equations under two constraints and the conditions for the existence of the free boundary points are given.The results can provide a qualitative and quantitative basis for the decision of the company.