Optimal Dividend And Capital Injections In Classical Risk Model Under Power Utility

In this paper,we mainly study the problem of optimal dividend and cap-ital injections in classical risk model with transaction costs under powerutility We characterize the value function of maximizing the total dis-counted utility of dividend payments minus the discounted value of capitalinjections Because of the transaction cost,we consider pulse stochasticcontrol problem in order to make the fixed costs at least We find thequasi--variational--inequalities which the value function sarisfy,and prove theverification theorem,at last,when claims are exponentially distributed,weobtain the optimal continuous and differentiable solution and the numericalsolution of optimal dividend strategy and capital injection strategy.