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

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.