Games of Economic Survival with Discrete- and Continuous-Income Processes

In this model the income process of a firm is assumed to be a homogeneous Markov process (discrete or continuous). One is interested in an optimal dividend strategy, i.e., a strategy that maximizes the expected sum of the discounted dividend payments. This paper derives general results in the case where the income process is skip free to the right; in particular, it establishes the factorization formula and shows it to be closely connected with the probability of ruin. The theory is illustrated by a numerical example.