Continuous-Time Portfolio Selection and Option Pricing under Risk-Minimization Criterion in an Incomplete Market

الملخص EN

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.