Some Divergence Properties of Asset Price Mod

We consider asset price processes Xt which are weak solutions of onedimensional stochastic di erential equations of the form dXt = b(t; Xt) dt + t Xt dWt: Such price models can be interpreted as non{lognormally{distributed generalizations of the geometric Brownian motion. We study properties of the I divergence between the law of the solution Xt and the corresponding drift{less measure (the special case = 1 is the relative entropy). This will be applied to some context in statistical information theory as well as to arbitrage theory and contingent claim valuation. For instance, the seminal option pricing theorems of Black-Scholes and Merton appear as a special case.