The classical risk model with constant interest and threshold strategy

In recent years, insurance risk models with dividend payments have been studied extensively. The threshold dividend strategy assumes that dividends are paid out at the maximal admissible rate whenever the surplus exceeds a certain threshold. In this paper, we consider the classical risk model with constant interest under the threshold strategy. We derive integro-differential equations for the expected discounted penalty function. In some special cases with exponential claims, we are able to obtain closed-form expressions for the expected discounted penalty function.