Stability of Sigma-Martingale Densities in L Log L Under an Equivalent Change of Measure

Abstract:     
An equivalent sigma-martingale measure (EsigmaMM) for a given stochastic process S is a probability measure R equivalent to the original measure P such that S is an R-sigma-martingale. Existence of an EsigmaMM is equivalent to a classical absence-of-arbitrage property of S, and is invariant if we replace the reference measure P with an equivalent measure Q. Now suppose that there exists an E!MM R for S such that the density dR dP is in L logL(P). Does this existence property also remain invariant if we replace P by some equivalent Q? We prove that the answer is Yes if one imposes instead of a global only a local integrability requirement.

Number of Pages in PDF File: 57

Keywords: sigma-martingale, equivalent martingale measures, Jacod decomposition, mathematical finance

JEL Classification: G10, C60

working papers series