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Monotone utility convergence

Part of: Mathematical economics Stochastic analysis

Published online by Cambridge University Press:  14 July 2016

Stefan Ankirchner
Stefan Ankirchner*
Affiliation:
Imperial College London
*
∗Postal address: Department of Mathematics, Imperial College London, London SW7 2AZ, UK. Email address: s.ankirchner@imperial.ac.uk
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Abstract

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We show that the maximal expected utility satisfies a monotone continuity property with respect to increasing information. Let be a sequence of increasing filtrations converging to , and let un(x) and u∞(x) be the maximal expected utilities when investing in a financial market according to strategies adapted to and , respectively. We give sufficient conditions for the convergence un(x) → u∞(x) as n → ∞. We provide examples in which convergence does not hold. Then we consider the respective utility-based prices, πn and π∞, of contingent claims under (Gtn) and (Gt∞). We analyse to what extent πn → π∞ as n → ∞.

Keywords

Utility maximisationinformationenlargement of filtrationsutility-based priceindifference price

MSC classification

Primary: 91B16: Utility theory
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 43 , Issue 3 , September 2006 , pp. 622 - 633
Copyright
© Applied Probability Trust 2006 

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