The Compound Poisson Risk Model with Interest and a Threshold Strategy

We consider the compound Poisson risk model with a constant force of interest and a threshold strategy. Under such a strategy, no dividends are paid if the insurer's surplus is below a certain threshold level. When the surplus is above the threshold level, part of the premium income and all of the interest income are paid out as dividends. The integro-differential equations for the Gerber-Shiu discounted penalty function and the expected discounted dividends are derived and solved. Closed-form expressions are given when the claim size is exponentially distributed. Numerical presentations are also provided for the case of exponential individual claim to illustrate the influence of force of interest and the safety loading on the expected discounted dividends.