CVaR pricing and hedging in Unit-Linked insurance products

This paper describes a way how to find the minimal seller’s price for a unit-linked insurance product in order to make the claim acceptable, under the assumption that information about the insurance process is only available at the time of maturity. For the general case, the price calculated here provides still an upper bound. Acceptability is defined through the CVaR criterion. Furthermore, the paper shows how to find the corresponding hedging strategy. We show how CVaR pricing is connected to earlier results of Föllmer/Leukert about minimization of Expected Shortfall, and apply and extend those results for the case of discrete insurance probabilities. We arrive at an algorithm which is straightforward and does not involve any optimization problem. For an example of a unit-linked survival insurance, we provide analytical formulas for the corresponding hedge, as well as an explicit numerical solutions for the CVaR price.