Equilibrium periodic dividend strategies with non-exponential discounting for spectrally positive Lévy processes

In the dual risk model, we study periodic dividend problem with a non-exponential discount function which results in time-inconsistent control problem. Viewing it within game theoretic framework, extend Hamilton-Jacobi-Bellman (HJB) system of equations from fixed terminal to time ruin and derive verification theorem, generalize theory classical optimal dividend. Under two special functions, obtain closed-form expressions equilibrium strategy corresponding value compound Poisson model. Finally, some numerical examples are presented illustrate impact parameters.