The Annals of Probability

On the minimal entropy martingale measure

Peter Grandits and Thorsten Rheinländer

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Abstract

Let X be a locally bounded semimartingale. Using the theory of \textit{BMO}-martingales we give a sufficient criterion for a martingale measure for X to minimize relative entropy among all martingale measures. This is applied to prove convergence of the q-optimal martingale measure to the minimal entropy martingale measure in entropy for $q\downarrow 1$ under the assumption that X is continuous and that the density process of some equivalent martingale measure satisfies a reverse $\mathit{LLogL}$\small -inequality.

Article information

Source
Ann. Probab., Volume 30, Number 3 (2002), 1003-1038.

Dates
First available in Project Euclid: 20 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1029867119

Digital Object Identifier
doi:10.1214/aop/1029867119

Mathematical Reviews number (MathSciNet)
MR1920099

Zentralblatt MATH identifier
1049.60035

Subjects
Primary: 28D20: Entropy and other invariants 60G48: Generalizations of martingales 60H05: Stochastic integrals 91B28

Keywords
Relative entropy martingale measures $\mathit{BMO}$-martingales

Citation

Grandits, Peter; Rheinländer, Thorsten. On the minimal entropy martingale measure. Ann. Probab. 30 (2002), no. 3, 1003--1038. doi:10.1214/aop/1029867119. https://projecteuclid.org/euclid.aop/1029867119


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