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Characterizing Attainable Claims: A New Proof

Part of: Mathematical economics Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Michael R. Tehranchi
Michael R. Tehranchi*
Affiliation:
University of Cambridge
*
∗Postal address: Statistical Laboratory, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, UK. Email address: m.tehranchi@statslab.cam.ac.uk
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Abstract

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This short note offers a new proof of the following fact: in a discrete-time arbitrage-free market model, a contingent claim is attainable if and only if its expected value is the same under all equivalent martingale measures. The proof is based on Rogers' (1994) proof of the Dalang-Morton-Willinger (1990) theorem.

Keywords

Fundamental theorem of asset pricingattainable contingent claim

MSC classification

Secondary: 60G42: Martingales with discrete parameter 91B25: Asset pricing models
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 4 , December 2010 , pp. 1013 - 1022
Copyright
Copyright © Applied Probability Trust 2010 

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