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Alexander Melnikov, Victoria Skornyakova

Quantile hedging and its application to life insurance

Keywords: equity-linked life insurance, pure endowment, flexible guarantee, quantile hedging, jump-diffusion model

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.

Statistics & Decisions, Oldenbourg Wissenschaftsverlag

Print ISSN: 0721-2631
Volume: 23, 04/2005
Pages: 301 - 316

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