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 co