Fair Dynamic Valuation of Insurance Liabilities: Merging Actuarial Judgement With Market- and Time-Consistency

Abstract In this paper, we investigate the fair valuation of insurance liabilities in a dynamic multi-period setting. We define a fair dynamic valuation as a valuation which is actuarial (mark-to-model for claims independent of financial market evolutions), market-consistent (mark-to-market for any hedgeable part of a claim) and time-consistent, extending the work of Dhaene et al. (2017) and Barigou and Dhaene (2019). We provide a complete hedging characterization for fair dynamic valuations. Moreover, we show how to implement fair dynamic valuations through a backward iterations scheme combining risk minimization methods from mathematical finance with standard actuarial techniques based on risk measures.