Date of Original Version
This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version is available at http://dx.doi.org/10.1016/j.spa.2013.06.017
Abstract or Description
Let Q and P be equivalent probability measures and let ψ be a Jdimensional vector of random variables such that dQ dP and ψ are defined in terms of a weak solution X to a d-dimensional stochastic differential equation. Motivated by the problem of endogenous completeness in financial economics we present conditions which guarantee that every local martingale under Q is a stochastic integral with respect to the J-dimensional martingale St , E Q[ψ|Ft]. While the drift b = b(t, x) and the volatility σ = σ(t, x) coefficients for X need to have only minimal regularity properties with respect to x, they are assumed to be analytic functions with respect to t. We provide a counter-example showing that this t-analyticity assumption for σ cannot be removed
Stochastic Processes and their Applications, 124, 1, 81-100.