Optimal dividend-financing strategies in a dual risk model with time-inconsistent preferences

In this paper, we consider an optimal dividend-financing problem for a company whose capital reserve is described by the dual of classical risk model. We assume that the manager of the company has time-inconsistent preferences, which are described by a quasi-hyperbolic discount function, and that financing is permitted to prevent the company from going bankrupt. The manager's objective is to maximize the expected cumulative dividend payments minus financing costs. We solve the optimization problems for a naive manager and a sophisticated manager, and obtain explicit solutions for both managers. Our results show that the manager with time-inconsistent preferences tends to pay out dividends earlier. We also present some economic implications and sensitivity analysis for our results.