Some divergence properties of asset price models (Q1613108)

Summary: We consider asset price processes \(X_t\) which are weak solutions of one-dimensional stochastic differential equations of the form \(dX_t = b(t; X_t) dt + st X_t dW_t\). Such price models can be interpreted as non-lognormally-distributed generalizations of the geometric Brownian motion. We study properties of the \(I_a\) -- between the law of the solution \(X_t\) and the corresponding drift-less measure (the special case \(a=1\) 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.