Moments of deficit duration and its proportion in general compound binomial model

Abstract

This paper discusses the deficit duration in the general compound binomial model. We derive the recursive formulas of moments of the deficit duration and its proportion in finite time with and without a dividend barrier, and use operators to design algorithms for finding their solutions. Under the condition of positive safety loading, we discuss the limit of deficit duration and show the convergence of moments of its proportion. In addition, the paper also discusses a sort of reinsurance strategy to significantly reduce the deficit duration. The proposed algorithms and reinsurance strategy are effective and are illustrated by numerical examples.