Fair dynamic valuation of insurance liabilities via convex hedging

A general class of fair dynamic valuations, which are model-consistent (mark-to-model), market-consistent (mark-to-market) and time-consistent, was introduced by Barigou et al. (2019) in a multi-period setting. In this paper, we generalize the convex hedging approach proposed in Dhaene et al. (2017) to a multi-period framework and investigate the realization of fair dynamic valuations via a convex hedge-based (CHB) approach. We show that the classes of fair dynamic valuations and CHB dynamic valuations are equivalent. Moreover, we show how to implement the CHB dynamic valuations based on two specific classes of convex hedging techniques, i.e. the quadratic and exponential convex hedging.