Quantile hedging and its application to life insurance

Summary The paper develops the method of quantile hedging in a two-factor jump-diffusion market. The exact formulae of the maximal successful hedging set for an option to exchange one asset for another are given. These results are applied to a class of equity-linked life insurance contracts called “pure endowments with a guarantee”. In our setting, the pay-off functions of these insurance contracts are equal to the maximum of two risky assets in a two-factor jump-diffusion model conditioned by the survival status of the insured. The first asset is responsible for the maximal size of future profits, while the second provides a flexible guarantee to the insured. Based on quantile hedging methodology and a generalized Margrabe's formula, the paper describes the valuation and risk management of such mixed finance-insurance instruments.