Finance and Stochastics

, Volume 19, Issue 2, pp 215–231 | Cite as

Fragility of arbitrage and bubbles in local martingale diffusion models

Article

Abstract

For any positive diffusion with minimal regularity, there exists a semimartingale with uniformly close paths that is a martingale under an equivalent probability. As a result, in models of asset prices based on such diffusions, arbitrage and bubbles alike disappear under proportional transaction costs or under small model mis-specifications. Thus, local martingale diffusion models of arbitrage and bubbles are not robust to small trading and monitoring frictions.

Keywords

Arbitrage Bubbles Transaction costs Local martingales 

Mathematics Subject Classification (2010)

91G10 62P05 

JEL Classification

G12 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsBoston UniversityBostonUnited States
  2. 2.School of Mathematical SciencesDublin City UniversityDublin 9Ireland
  3. 3.MTA Alfréd Rényi Mathematical InstituteBudapestHungary
  4. 4.School of MathematicsUniversity of EdinburghEdinburghUnited Kingdom

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