Best-Estimate Claims Reserves in Incomplete Markets

Abstract

We give a rigorous definition of best-estimate reserves for insurance liabilities in a general multiperiod financial market setting. In this general multiperiod financial market setting we describe payoff spaces and optimal dynamic hedging strategies. Based on this optimal dynamic hedging strategies we define best-estimate reserves for insurance liabilities. One crucial observation is that we need the notion of optimal hedging and state-price deflators because there does not necessarily exist an equivalent probability measure under which best-estimate reserves can be calculated.

Keywords: best-estimate reserves, dynamic hedging, sequential local risk minimization, state-price deflator, incomplete market, technical provisions, risk margin

JEL Classification: G22, G13, G18, G38, D46, C59