Reinsurance Optimization: Minimizing the Ruin Probability for both Cedent and Reinsurer

This study considers a reinsurance market with two participants, one taking the role of first line insurer and the other taking the role of reinsurer. The two firms have conflicting interests, in the sense that they both seek to absorb the highest proportion of the insurance premium possible, while also taking on the least amount of risk they can. As such, we consider a game where the first line insurer and the reinsurer aim to minimize their respective ruin probabilities. We define the surplus processes for each involved party and derive a set of integro-differential equations that describe the behaviour of their ruin probabilities. Numerical illustrations for this model are provided. Then, we present the Pareto equilibrium conditions for this market and suggest one possible approach to implement the numerical solution of the problem.