On a generalization of the expected discounted penalty function in a discrete-time insurance risk model

In this paper, we propose a generalization of the expected discounted penalty function and analyze the proposed analytic tool in the framework of the compound binomial model with a general premium rate c (c is an element of N+) received per period. We derive an explicit expression for this generalized analytic tool in terms of the zeros of a matrix determinant. We then examine the original expected discounted penalty function in the compound binomial model with a general premium rate c, generalizing the results of Cheng et al. (Insur Math. Econ. 2000; 26:239-250) in the framework of the compound binomial model with a unit premium rate. A numerical example is then considered to compare the original expected discounted penalty function with its generalized analytic tool. Copyright (C) 2008 John Wiley & Sons, Ltd.