Practical and theoretical aspects of market-consistent valuation and hedging of insurance liabilities

In this paper we deal with market-consistent valuation and hedging of insurance cash flows. We start with recalling traditional actuarial and financial pricing principles and we show how to integrate them into one arbitrage-free principle which leads to market-consistent valuation of the cash flows. Integrated actuarial and financial valuation is justified by referring to Solvency II Directive and discussing its key points related to market-consistent valuation. As an arbitrage-free pricing principle requires specification of an equivalent martingale measure, we characterize all equivalent martingale measures in a very general combined insurance and financial model. This full characterization allows us to price all claims contingent on the financial and insurance risks. We also deal with static and dynamic hedging of insurance liabilities in our general model. We derive an investment portfolio consisting of a bond, a stock and a mortality bond which can be used by a life insurance company to hedge its payment process contingent on the financial and insurance risk. The goal is to unify practical and theoretical aspects of market-consistent valuation and hedging and to state general results relevant to insurance applications.