  We show that our generalization of the Black-Scholes partial differential
equation (pde) for nontrivial diffusion coefficients is equivalent to a
Martingale in the risk neutral discounted stock price. Previously, this was
proven for the case of the Gaussian logarithmic returns model by Harrison and
Kreps, but we prove it for much a much larger class of returns models where the
diffusion coefficient depends on both returns x and time t. That option prices
blow up if fat tails in logarithmic returns x are included in the market
dynamics is also explained.
