EFFICIENT HEDGING FOR DEFAULTABLE SECURITIES AND ITS APPLICATION TO EQUITY-LINKED LIFE INSURANCE CONTRACTS

Alexander Melnikov and Amir Nosrati ()
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Alexander Melnikov: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
Amir Nosrati: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada

International Journal of Theoretical and Applied Finance (IJTAF), 2015, vol. 18, issue 07, 1-28

Abstract: The paper deals with efficient hedging problem for defaultable securities with multiple default times and nonzero recovery rates. First, we convert the efficient hedging problem into a Neyman–Pearson problem with composite hypothesis against a simple alternative. Then we apply nonsmooth convex duality to provide a solution in the framework of a “defaultable” Black–Scholes model. Moreover, in the case of zero recovery rates, we find a closed form solution for the problem. As an application, it is shown how to use such type of results in pricing equity-linked life insurance contracts. The results are also demonstrated by some numerical examples.

Keywords: Efficient hedging; nonsmooth convex duality; Frechet derivative; Gateaux derivative; default time; superhedging; equity-linked life insurance contract (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0219024915500478

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