The purpose of this paper is studying the valuation of European option
prices under jump-diusion processes. Due to the jump part, the market is
incomplete and so it is impossible to construct a hedging portfolio with stocks
and riskless assets. Contrary to the case of a complete market in which only one
equivalent martingale measure exists, there are in nite numbers of equivalent
martingale measures in an incomplete market. Our research here is focusing
on risk minimizing hedging strategy and its associated minimal martingale
measure under the jump-diusion processes. Based on this risk minimizing
hedging strategy, we characterize the dynamics of a risky asset and derive the
valuation formula for an option price. The main contribution of this paper is
to obtain an analytical formula for a European option price under the jump di
fusion processes using the minimal martingale measure.

