Deficit duration and its proportion in the discrete-time Sparre Andersen risk model

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