带资本注入、交易费和税的经典风险模型的最优联合分红与注资策略

摘要

In the classical Cramér-Lundberg model in risk theory the problem of finding the optimal dividend strategy and optimal dividend return function is a widely discussed topic.In the present paper,we discuss the problem of maximizing the expected discounted net dividend payments minus the expected discounted costs of injecting new capital,in the Cramér-Lundberg model with proportional taxes and fixed transaction costs imposed each time the dividend is paid out and with both fixed and proportional transaction costs incurred each time the capital injection is made.Negative surplus or ruin is not allowed.By solving the corresponding quasi-variational inequality,we obtain the analytical solution of the optimal return function and the optimal joint dividend and capital injection strategy when claims are exponentially distributed.%在风险理论中,经典Cramér-Lundberg模型的最优红利策略和最优红利收益函数问题是一个被广泛讨论的话题.本文讨论一类Cramér-Lundberg模型:其在分红时伴随比例赋税与固定交易费,注资时伴随比例罚金与固定交易费,并研究了其净红利收益与注入资本之差的预期贴现值的最大化问题.这里我们不允许负盈余或破产的发生.通过解相应的拟变分不等式,在索赔为指数分布时,得到了最优收益函数和最优联合分红与注资策略的解析解.