Integral representation of martingales motivated by the problem of endogenous completeness in financial economics

6Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.

Abstract

Let Q and P be equivalent probability measures and let ψ be a J-dimensional 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 Stδ EQ[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. © 2013 Elsevier B.V. All rights reserved.

Cite

CITATION STYLE

APA

Kramkov, D., & Predoiu, S. (2014). Integral representation of martingales motivated by the problem of endogenous completeness in financial economics. Stochastic Processes and Their Applications, 124(1), 81–100. https://doi.org/10.1016/j.spa.2013.06.017

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free