Fair dynamic valuation of insurance liabilities: a loss averse convex hedging approach

Hedging techniques have been widely adopted in market-consistent or fair valuation approach required by recent solvency regulations, to take into account the market prices of the hedgeable parts of insurance liabilities. In this study, we investigate the fair dynamic valuation of insurance liabilities, which are model-consistent (mark-to-model), market-consistent (mark-to-market), and time-consistent, as proposed by Barigou et al. (2019) in a multi-period setting. We introduce the loss averse convex hedging technique, which 'punishes' loss outcomes more than gain outcomes. We prove that fair dynamic valuations are equivalent to the class of loss averse convex hedge-based valuation. Moreover, we propose and provide a complete characterization of loss averse mean-variance hedging and show how to implement loss averse mean-variance hedge-based dynamic valuations using numerical examples.