Optimal combined dividend and reinsurance policies under interest rate in Lévy markets

Abstract

Abstract:A combined dividend and risk control problem is presented and investigated in this paper. The risk of the insurance firm is controlled by using a proportional reinsurance policy. It is considered that the evolution of the cash reserves of the firm is driven by a generalised Itô-Lévy process. The surplus cash reserves earn interest at a constant rate. The objective of the firm is to maximise the total expected discounted dividends paid out to share holders. The situation is modelled as an impulse-classical control problem. We manage to construct the value function and the optimal impulse control. The existence and uniqueness of an optimal classical control is proved.