# On the martingale property of stochastic exponentials

@article{Wong2004OnTM,
title={On the martingale property of stochastic exponentials},
author={Bernard Wong and Chris C. Heyde},
journal={Journal of Applied Probability},
year={2004},
volume={41},
pages={654 - 664}
}
• Published 1 September 2004
• Mathematics
• Journal of Applied Probability
We present a necessary and sufficient condition for a stochastic exponential to be a true martingale. It is proved that the criteria for the true martingale property are related to whether a related process explodes. An alternative and interesting interpretation of this result is that the stochastic exponential is a true martingale if and only if under a ‘candidate measure’ the integrand process is square integrable over time. Applications of our theorem to problems arising in mathematical…
This note studies the martingale property of a nonnegative, continuous local martingale Z, given as a nonanticipative functional of a solution to a stochastic differential equation. The condition
We introduce a transform on the class of stochastic exponentials for d-dimensional Brownian motions. Each stochastic exponential generates another stochastic exponential under the transform. The new
• Mathematics
• 2009
The stochastic exponential $${Z_t= {\rm exp}\{M_t-M_0-(1/2)\langle M,M\rangle_t\}}$$ of a continuous local martingale M is itself a continuous local martingale. We give a necessary and sufficient
• Mathematics
• 2006
Pricing in mathematical finance often involves taking expected values under different equivalent measures. Fundamentally, one needs to first ensure the existence of ELMM, which in turn requires that
• Mathematics
• 2006
We find a simple expression for the probability density of $\int \exp (B_s - s/2) ds$ in terms of its distribution function and the distribution function for the time integral of $\exp (B_s + s/2)$.
• Mathematics
• 2011
In this note we re-examine the analysis of the paper "On the martingale property of stochastic exponentials" by B. Wong and C.C. Heyde, Journal of Applied Probability, 41(3):654-664, 2004. Some
• Mathematics
• 2010
We establish existence of exponential moments and the validity of the affine transform formula for affine jump-diffusions with a general closed convex state space. This extends known results for