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Mathematics and Financial Economics

, Volume 12, Issue 4, pp 589–614 | Cite as

Arbitrage and utility maximization in market models with an insider

  • Huy N. Chau
  • Wolfgang J. Runggaldier
  • Peter Tankov
Article
  • 46 Downloads

Abstract

We study arbitrage opportunities, market viability and utility maximization in market models with an insider. Assuming that an economic agent possesses an additional information in the form of an \(\mathscr {F}_T\)-measurable discrete random variable G, we give criteria for the no unbounded profits with bounded risk property to hold, characterize optimal arbitrage strategies, and prove duality results for the utility maximization problem faced by the insider. Examples of markets satisfying NUPBR yet admitting arbitrage opportunities are provided. For the case when G is a continuous random variable, we consider the notion of no asymptotic arbitrage of the first kind (NAA1) and give an explicit construction for unbounded profits if NAA1 fails.

Keywords

Initial enlargement of filtration Optimal arbitrage No unbounded profits with bounded risk Incomplete markets Hedging Utility maximization 

JEL Classification

G14 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Huy N. Chau
    • 1
  • Wolfgang J. Runggaldier
    • 2
  • Peter Tankov
    • 3
  1. 1.Alfréd Rényi Institute of MathematicsHungarian Academy of SciencesBudapestHungary
  2. 2.Department of MathematicsUniversity of PaduaPaduaItaly
  3. 3.CREST-ENSAE Paris TechPalaiseauFrance

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