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The Markov Chain Market

Published online by Cambridge University Press:  17 April 2015

Ragnar Norberg
Ragnar Norberg*
Affiliation:
London School of Economics and Political Science, Department of Statistics, Houghton Street, London WC2A 2AE, United Kingdom, E-mail: R.Norberg@lse.ac.uk
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Abstract

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We consider a financial market driven by a continuous time homogeneous Markov chain. Conditions for absence of arbitrage and for completeness are spelled out, non-arbitrage pricing of derivatives is discussed, and details are worked out for some cases. Closed form expressions are obtained for interest rate derivatives. Computations typically amount to solving a set of first order partial differential equations. An excursion into risk minimization in the incomplete case illustrates the matrix techniques that are instrumental in the model.

Keywords

Continuous time Markov chainsMartingale analysisArbitrage pricing theoryRisk minimizationUnit linked insurance
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 33 , Issue 2 , November 2003 , pp. 265 - 287
Copyright
Copyright © ASTIN Bulletin 2003

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