  Current approaches to fair valuation in insurance often follow a two-step
approach, combining quadratic hedging with application of a risk measure on the
residual liability, to obtain a cost-of-capital margin. In such approaches, the
preferences represented by the regulatory risk measure are not reflected in the
hedging process. We address this issue by an alternative two-step hedging
procedure, based on generalised regression arguments, which leads to portfolios
that are neutral with respect to a risk measure, such as Value-at-Risk or the
expectile. First, a portfolio of traded assets aimed at replicating the
liability is determined by local quadratic hedging. Second, the residual
liability is hedged using an alternative objective function. The risk margin is
then defined as the cost of the capital required to hedge the residual
liability. In the case quantile regression is used in the second step, yearly
solvency constraints are naturally satisfied; furthermore, the portfolio is a
risk minimiser among all hedging portfolios that satisfy such constraints. We
present a neural network algorithm for the valuation and hedging of insurance
liabilities based on a backward iterations scheme. The algorithm is fairly
general and easily applicable, as it only requires simulated paths of risk
drivers.
