Investment and dividends payment under fixed and proportional transaction costs

摘要

This paper deals with the dividend optimization problem of a firm with stochastic return on investment in presence of fixed and proportional transaction costs.Due to the presence of a fixed transaction cost,the mathematical problem reduces to classical impulse control problem.Using the stochastic impulse control approach,we transform the stochastic control problem into a quasi-variational inequality for a second-order nonlinear integro-differential equation.Under risk neutral assumption for the insurer,the explicit solution for the optimal value function is derived.Furthermore,the optimal policy is obtained under some assumptions.Finally,we discuss the moment of the time to ruin when the optimal strategy is employed.