Reinsurance of multiple risks with generic dependence structures

TL;DR

This paper investigates optimal reinsurance strategies for multiple dependent risks without assuming a specific dependence structure, establishing existence, characterizing optimal contracts, and providing a numerical solution approach.

Contribution

It introduces a general framework for optimal reinsurance with arbitrary dependence structures and characterizes the nature of optimal contracts, including conditions for classical solutions.

Findings

Optimal treaties exist within a class of independent randomized contracts.

Under mild assumptions, optimal contracts are non-randomized.

A numerical scheme is proposed to solve the optimality conditions.

Abstract

We consider the optimal reinsurance problem from the point of view of a direct insurer owning several dependent risks, assuming a maximal expected utility criterion and independent negotiation of reinsurance for each risk. Without any particular hypothesis on the dependency structure, we show that optimal treaties exist in a class of independent randomized contracts. We derive optimality conditions and show that under mild assumptions the optimal contracts are of classical (non-randomized) type. A specific for mof the optimality conditions applies in that case. We present a numerical scheme to solve the optimality conditions.