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Insider Models with Finite Utility in Markets with Jumps

  • Arturo Kohatsu-Higa
  • Makoto Yamazato
Article

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.

Keywords

Asymmetric markets Markets driven by Lévy processes Enlargement of filtrations 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematical SciencesRitsumeikan University1-1-1 Nojihigashi, KusatsuJapan
  2. 2.Department of Mathematics, Faculty of ScienceUniversity of the RyukyusSenbaru 1, Nishihara-choJapan

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