The Gerber–Shiu Discounted Penalty Function for the Bi-Seasonal Discrete Time Risk Model

Abstract

In this work, the discrete time risk model with two seasons is considered. In such model, the claims repeat with time periods of two units, i.e. claim distributions coincide at all even instants and at all odd instants. Our purpose is to derive an algorithm for calculating the values of the particular case of the Gerber–Shiu discounted penalty function $\mathbb{E}({\mathrm{e}^{-\delta T}}{\mathbb{1}_{\{T<\infty \}}})$, where T is the time of ruin, and δ is a constant nonnegative force of interest. Theoretical results are illustrated by some numerical examples.