Optimal dividend strategies with time-inconsistent preferences and transaction costs in the Cramér-Lundberg model

•A dynamic time-inconsistent dividend problem with transaction costs is studied.•The optimization problem is solved for both naive and sophisticated managers.•Explicit optimal strategies and value functions are derived with mild conditions.•Some theoretical and numerical analyses are presented to illustrate our results.•Some examples and interesting phenomena are provided.

This paper considers the optimal dividend strategies for an insurance company with transaction costs and time-inconsistent preferences. We assume that the company's surplus is modeled by a compound Poisson process and that the manager is either naive or sophisticated. We tackle the optimal dividend problem when the claim sizes belong to a certain class of distributions and the optimal dividend strategies are of the lump sum type. Our results indicate that a time-inconsistent manager tends to pay out dividends earlier and more frequently than a time-consistent manager, but with smaller dividend amounts. We also present the special case where claim sizes follow mixed exponential distribution to illustrate our results and to analyze the effect of time-inconsistency and transaction costs on the optimal dividend strategies.