Ragnar Norberg

Institut de Science Financiere et d'Assurances (ISFA), Universite Lyon 1

An actuarial perspective on hedging

Abstract: An investment strategy consists of a process of portfolio weights (defined as usual) and a cost process representing deposits into and withdrawals from the portfolio. The investment strategy is a hedge of a contractual payment stream (e.g. defined by an insurance contract) if the payments are currently deposited on or withdrawn from the portfolio as they are due. The purpose of the hedge is stated as a optimization criterion for the investment strategy. Certain quadratic loss criteria lead to the same optimal portfolio weights but different optimal cost functions, special cases being mean-variance hedging and risk minimization. An attempt is made to incorporate Solvency II in the set-up. So far the theory dealt with optimal hedging with a given set of available traded assets. We finish by discussing the design of the very assets (viz. insurance derivatives), the purpose being to minimize the average hedging error across a population of hedgers pursuing optimal individual hedging strategies.