Research On The Dividend And Other Issues Of The Dual Risk Model

In this paper,we mainly introduced two kinds of dual risk models: the dual risk model with penalty payments and the dual risk model with diffusion and time-inconsistent preferences.Dividend and other related problems are studied.Firstly,we study the optimal dividend problem with penalty payments in the dual model.We derive the HJB equation and the verification theorem.When the profits follow an exponential distribution,we obtain the optimal dividend strategies and explicit solutions for exponential and linear penalty payments,respectively.Secondly,we consider the optimal dividend and capital injection problems in a dual risk model with diffusion and time-inconsistent preferences.And the manager's preferences are described by a quasi-hyperbolic discount function.When the profits follow an exponential distribution,the optimal strategies and the explicit solutions are obtained.We find that the managers with time-inconsistent preferences tend to pay out dividends earlier than the managers with time-consistent preferences.