Optimal Dividend Strategies For A Compound Poisson Process With Capital Injections And Exponential Utility

We mainly consider the optimal dividend strategies in the classical model with capital injections. The company control dividends with exponen-tial utility function.Especially,we discuss the capital should be injected when or before the surplus become negative for claims.We characterize the value function of maximizing the total discounted utility of dividend payments minus the penalized discounted capital injections.Then we de-rive the Hamilton-Jacobi-Bellman equation for the problem and how the optimal strategies is a barrier strategy.Analyze the properties of the value function and derive the solution for exponential claim amounts.