CDF formulation for solving an optimal reinsurance problem

Abstract

An innovative cumulative distribution function (CDF)-based method is proposed for deriving optimal reinsurance contracts to maximize an insurer’s survival probability. The optimal reinsurance model is a non-concave constrained stochastic maximization problem, and the CDF-based method transforms it into a functional concave programming problem of determining an optimal CDF over a corresponding feasible set. Compared to the existing literature, our proposed CDF formulation provides a more transparent derivation of the optimal solutions, and more interestingly, it enables us to study a further complex model with an extra background risk and more sophisticated premium principle.