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Finance and Stochastics
Published in: Finance and Stochastics 4/2012

01-10-2012

Horizon dependence of utility optimizers in incomplete models

Authors: Kasper Larsen, Hang Yu

Published in: Finance and Stochastics | Issue 4/2012

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Abstract

This paper studies the utility maximization problem with changing time horizons in the incomplete Brownian setting. We first show that the primal value function and the optimal terminal wealth are continuous with respect to the time horizon T. Secondly, we exemplify that the expected utility stemming from applying the T-horizon optimizer on a shorter time horizon S<T may fail to converge to the T-horizon value as S↑T. Finally, we provide necessary and sufficient conditions preventing the existence of this phenomenon.
previous article The fundamental theorem of asset pricing under transaction costs

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Appendix
Available only for authorised users
Footnotes
1
In the case r t =0, i.e., \(S^{(0)}_{t} =1\) for all \(t\in[0,\overline{T}]\), [6] illustrate that Assumption 2.1 is strictly stronger than the no free lunch with vanishing risk condition.
 
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Metadata
Title
Horizon dependence of utility optimizers in incomplete models
Authors
Kasper Larsen
Hang Yu
Publication date
01-10-2012
Publisher
Springer-Verlag
Published in
Finance and Stochastics / Issue 4/2012
Print ISSN: 0949-2984
Electronic ISSN: 1432-1122
DOI
https://doi.org/10.1007/s00780-012-0171-6

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