Insider Models with Finite Utility in Markets with Jumps

Insider Models with Finite Utility in Markets with Jumps In this article we consider, under a Lévy process model for the stock price, the utility optimization problem for an insider agent whose additional information is the final price of the stock blurred with an additional independent noise which vanishes as the final time approaches. Our main interest is establishing conditions under which the utility of the insider is finite. Mathematically, the problem entails the study of a “progressive” enlargement of filtration with respect to random measures. We study the jump structure of the process which leads to the conclusion that in most cases the utility of the insider is finite and his optimal portfolio is bounded. This can be explained financially by the high risks involved in models with jumps. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Insider Models with Finite Utility in Markets with Jumps

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Publisher
Springer-Verlag
Copyright
Copyright © 2011 by Springer Science+Business Media, LLC
Subject
Mathematics; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Calculus of Variations and Optimal Control; Optimization; Numerical and Computational Physics; Systems Theory, Control
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-011-9137-x
Publisher site
See Article on Publisher Site

Abstract

In this article we consider, under a Lévy process model for the stock price, the utility optimization problem for an insider agent whose additional information is the final price of the stock blurred with an additional independent noise which vanishes as the final time approaches. Our main interest is establishing conditions under which the utility of the insider is finite. Mathematically, the problem entails the study of a “progressive” enlargement of filtration with respect to random measures. We study the jump structure of the process which leads to the conclusion that in most cases the utility of the insider is finite and his optimal portfolio is bounded. This can be explained financially by the high risks involved in models with jumps.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Oct 1, 2011

References

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