Fair valuation of insurance liabilities: Merging actuarial judgement and market-consistency

In this paper, we investigate a single period framework for the fair valuation of the liabilities related to an insurance policy or portfolio.We de ne a fair valuation as a valuation which is both market-consistent (mark-to-market for hedgeable claims)and actuarial (mark-to-model for unhedgeable claims). We introduce the class of hedge-based valuations, where in a rst step of the valuation process, a best hedge for the liability is set up, based on the traded assets in the market, while in a second step, the remaining part of the claim is valuated via an actuarial valuation. We also introduce the class of two-step valuations, the elements of which are closely related to the two-step valuations which were introduced in Pelsser and Stadje (2014). We show that the 3 classes of fair, hedge-based and two-step valuations are identical.