Optimal Policies for Payment of Dividends through a Fixed Barrier at Discrete Time

摘要

In this paper a discrete-time reserve process with a fixed barrier is presented and modelled as a discounted Markov Decision Process. The non-payment of dividends is penalized. The minimization of this penalty results in an optimal control problem. This work focuses on determining the sequence of premiums that minimize penalty costs, and obtaining a rate for the probability of ruin to ensure a sustainable reserve operation.