Reinsurance in arbitrage-free markets

Abstract

The paper studies dynamic reinsurance policies in the continuous Lundberg model, where claims, premiums and interest rates are stochastic processes. The main purpose of the paper is to study the consequences of arbitrage-free markets for the premium calculation of arbitrary reinsurance contracts like stop loss or excess loss. An explicit formula is derived for the stop-loss contract when the claim process is Compound Poisson. Conditions are given when Pareto-optimal allocations of the total risk in an economy can be achieved through markets for proportional risk sharing.