Quantile hedging for equity-linked contracts

We consider an equity-linked contract whose payoff depends on the lifetime of the policy holder and the stock price. We provide the best strategy for an insurance company assuming limited capital for the hedging. The main idea of the proof consists in reducing the construction of such strategies for a given claim to a problem of superhedging for a modified claim, which is the solution to a static optimization problem of the Neyman–Pearson type. This modified claim is given via some sets constructed in an iterative way. Some numerical examples are also given.