Abstract: The price of underlying assets follows a jump-diffusion process. We introduce the dynamic measure of risk to the incomplete market. We have acquired optimal replication of contingent claim in the auxilizar finance market which is induced by a risk neutral probability measure. With an application clark formula the paper provides the optimal hedging strategy for a contingent claim.

Key words: contingent claim, hedging strategy, incomplete market, a generalized clark formula, jump-diffusion process