Fair valuation of insurance liabilities via mean-variance hedging in a multi-period setting

A general class of fair valuations which are both market-consistent (mark-to-market for any hedgeable part of a claim) and actuarial (mark-to-model for any claim that is independent of financial market evolutions) was introduced in Dhaene et al. [Insurance: Mathematics & Economics, 76, 14–27 (2017)] in a single period framework. In particular, the authors considered mean-variance hedge-based (MVHB) valuations where fair valuations of insurance liabilities are expressed in terms of mean-variance hedges and actuarial valuations. In this paper, we generalize this MVHB approach to a multi-period dynamic investment setting. We show that the classes of fair valuations and MVHB valuations are equivalent in this generalized setting. We derive tractable formulas for the fair valuation of equity-linked contracts and show how the actuarial part of their MVHB valuation decomposes into a diversifiable and a non-diversifiable component.