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

Abstract

A general class of fair valuations which are both market-consistent (mark-tomarket 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.

Valuation of Hybrid Financial and Actuarial Products in Life Insurance by a Novel Three-Step Method

“…Secondly, hybrid products based on a combination of actuarial and financial components are more and more present on the markets (for instance, life insurance products with optional payoffs) and require then a new adjusted valuation principle. Different principles have been proposed in the literature in order to price these hybrid products (see, e.g., Møller, 2002;Malamud et al, 2008;Möhr, 2011;Pelsser and Stadje, 2014;Pelsser and Ghalehjooghi, 2016;Dhaene et al, 2017;Barigou and Dhaene, 2019;Delong et al, 2019a,b;Engsner et al, 2020 and many others). Our article contributes to this literature by proposing a novel decomposition method with a clear separation of risks that are hedgeable on financial markets, risks that can be reduced by pooling, and a remaining part evaluated by taking into account solvency guidelines.…”

Fair Valuation of Insurance Liability Cash-Flow Streams in Continuous Time: Applications

“…Pelsser 2010and Pelsser and Ghalehjooghi (2016) propose a completely different one-period valuation operator , called a two-step valuation operator. Dhaene et al (2017) and Barigou and Dhaene (2019) use the one-period valuation operator (3.11) but they consider static hedging strategies. Let us compare our hedging strategy (3.4) and the valuation operator (3.12) with the hedging strategies and the valuation operators from the papers mentioned.…”

“…Dhaene et al 2017and Barigou and Dhaene (2019) suggest to apply the valuation operator (3.11) and find the static hedging portfolio by solving the quadratic hedging problem (3.2) under the real-world measure P. From Theorem 1 from Barigou and Dhaene (2019), the static hedging strategy and the value of the hedging portfolio are given by…”

“…It is clear that our valuation operator yields a lower price than the operator from Dhaene et al (2017) and Barigou and Dhaene (2019) since we allow for dynamic hedging in continuous time and the hedging strategy is updated with the current information on the insurance risk (the number of survivors). As expected, the one-period valuation operator suggested by Pelsser (2010) and Pelsser and Ghalehjooghi (2016) is different from ours.…”

“…Fair valuation of insurance liabilities, which combines market-consistent and actuarial valuations, is also investigated in Pelsser (2010), Pelsser and Stadje (2014), Pelsser and Ghalehjooghi (2016), Happ et al (2015), Engsner et al (2017), , , Möhr (2011), Dhaene et al (2017), Barigou and Dhaene (2019) and Barigou et al (2018). In all these papers, a multi-period model and an iterative valuation operator are considered.…”