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研究了复合Poisson模型带比例与固定费用的最优分红与注资问题.每次分红与注资时,存在比例及固定的交易费用.通过控制分红与注资的时刻以及分红及注资量,实现破产前分红减注资的折现期望的最大化.由于存在固定交易费用,问题为一个脉冲控制问题.根据问题的参数不同,问题的解可分为两大类.一类解为只进行最优分红不需要注资,而另一类情况需要注资.需要注资时,最优注资策略由最优注资上界以及最优注资下界描述.当赤字小于最优注资下界的绝对值时,进行注资.最后,在理赔为指数分布时明确地给出了两类共七种最优策略以及值函数的形式.从而彻底地解决了该问题.
The paper studies the optimal dividend and capital injection problem of compound Poisson model with proportional and fixed costs.Each dividend and capital injection has a certain proportion and fixed transaction costs.By controlling the time of dividend and capital injection as well as the dividend and capital injection, Since the existence of fixed transaction costs, the problem is a pulse control problem.According to the different parameters of the problem, the solution of the problem can be divided into two categories. A class solution is only the optimal dividend is not required When the capital injection is needed, the optimal capital injection strategy is described by the upper limit of the optimal capital injection and the lower limit of the optimal capital injection.When the deficit is less than the absolute value of the lower limit of the optimal capital injection, capital injection is carried out.Finally, For the exponential distribution, two kinds of optimal strategies and the form of the value function are clearly given, which completely solves the problem.