Deficit Duration and Its Proportion in the Discrete-Time Sparre Andersen Risk Model

This paper discusses the moments of deficit duration and its proportion in the discrete-time Sparre Andersen risk model with relative positive safety loading. We use CDF of claim inter-arrival times to construct a sequence of random variables in 0-1 distribution basis with and without claim in per unit time. This sequence is then used to derive the recursive formulas for the moments of the deficit duration and its proportion in finite time with and without a dividend barrier. In addition, we use operators to design algorithms for finding their solutions.