The Expected Discounted Penalty Function with Random Income under Stochastic Discount Interest Force
We study the delayed risk model with random premium income. The premium process is not a linear function of time in contrast with the classical model, but a Poisson process which is also independent of the claim process. We shall consider the case where the discount interest process is no longer a constant in comparison with the classical expected discounted penalty function, but a stochastic interest driven by Poisson process and Wiener process. The expected discounted penalty function in the delayed renewal model is expressed in terms of the corresponding Gerber-Shiu function in the ordinary renewal model. The obtained results can be viewed as the discrete analogy of the classical Sparre-Anderson risk model.
Zhenyu Du and X.B Sun
W. G. Yu and Z. Liu, "The Expected Discounted Penalty Function with Random Income under Stochastic Discount Interest Force", Advanced Materials Research, Vols. 113-116, pp. 378-381, 2010