On the martingale property of stochastic exponentials

Date

2004

Authors

Wong, Bernard
Heyde, C C

Journal Title

Journal ISSN

Volume Title

Publisher

Applied Probability Trust

Abstract

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 finance are also given.

Description

Keywords

Keywords: Equivalent local martingale measure; Explosion; Martingale property

Citation

Source

Journal of Applied Probability

Type

Journal article

Book Title

Entity type

Access Statement

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DOI

10.1239/jap/1091543416

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