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The Minimal Entropy Martingale Measure for Exponential Markov Chains

Part of: Markov processes

Published online by Cambridge University Press:  30 January 2018

Young Lee  and
Thorsten Rheinländer
Young Lee*
Affiliation:
Deutsche Bank AG and London School of Economics
Thorsten Rheinländer*
Affiliation:
Vienna University of Technology
*
∗ Postal address: Deutsche Bank AG, 1 Great Winchester Street, London EC2N 2DB, UK. Email address: young.lee@db.com
∗∗ Postal address: Financial and Actuarial Mathematics, Vienna University of Technology, Wiedner Hauptstraße 8/105-1, 1040 Vienna, Austria. Email address: rheinlan@fam.tuwien.ac.at
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Abstract

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In this article we investigate the minimal entropy martingale measure for continuous-time Markov chains. The conditions for absence of arbitrage and existence of the minimal entropy martingale measure are discussed. Under this measure, expressions for the transition intensities are obtained. Differential equations for the arbitrage-free price are derived.

Keywords

Continuous-time Markov chainrelative entropymartingale measure

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 2 , June 2013 , pp. 344 - 358
Copyright
© Applied Probability Trust 

Footnotes

The views expressed in this paper are those of the author and do not necessarily reflect the position of Deutsche Bank AG.

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