2013/12/02 by Rodrigo S. Targino, Gareth W. Peters, Targino, Rodrigo S. +5
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Social Sciences · #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Economics and business #Insurance, Mortality, Demography, Risk Management #Probability and Risk Models #Risk Management (q-fin.RM) #Statistical Distribution Estimation and Applications #Statistical Finance (q-fin.ST) #q-fin.RM #q-fin.ST #stat.CO
paper · pdf · doi:10.48550/arxiv.1312.0424
arxiv created 2013/12/02 · openalex publication_date 2013/12/02 · arxiv updated 2013/12/03 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
In this paper we study a class of insurance products where the policy holder has the option to insure k of its annual Operational Risk losses in a horizon of T years. This involves a choice of k out of T years in which to apply the insurance policy coverage by making claims against losses in the given year. The insurance product structure presented can accommodate any kind of annual mitigation, but we present three basic generic insurance policy structures that can be combined to create more complex types of coverage. Following the Loss Distributional Approach (LDA) with Poisson distributed annual loss frequencies and Inverse-Gaussian loss severities we are able to characterize in closed form analytical expressions for the multiple optimal decision strategy that minimizes the expected Operational Risk loss over the next T years. For the cases where the combination of insurance policies and LDA model does not lead to closed form expressions for the multiple optimal decision rules, we also develop a principled class of closed form approximations to the optimal decision rule. These approximations are developed based on a class of orthogonal Askey polynomial series basis expansion representations of the annual loss compound process distribution and functions of this annual loss.