We study option pricing with risk-minimization criterion in an incomplete market where the dynamics of the risky underlying asset are governed by a jump diffusion equation. We obtain the Radon-Nikodym derivative in the minimal martingale measure and a partial integrodifferential equation (PIDE) of European call option. In a special case, we get the exact solution for European call option by Fourier transformation methods. Finally, we employ the pricing kernel to calculate the optimal portfolio selection by martingale methods.
"Continuous-Time Portfolio Selection and Option Pricing under Risk-Minimization Criterion in an Incomplete Market." J. Appl. Math. 2013 1 - 11, 2013. https://doi.org/10.1155/2013/175269