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When does fractional Brownian motion not behave as a continuous function with bounded variation?

Author

Listed:
  • Azmoodeh, Ehsan
  • Tikanmäki, Heikki
  • Valkeila, Esko

Abstract

If we compose a smooth function g with fractional Brownian motion B with Hurst index , then the resulting change of variables formula (or Itô formula) has the same form as if fractional Brownian motion was a continuous function with bounded variation. In this note we prove a new integral representation formula for the running maximum of a continuous function with bounded variation. Moreover we show that the analogy to fractional Brownian motion fails.

Suggested Citation

  • Azmoodeh, Ehsan & Tikanmäki, Heikki & Valkeila, Esko, 2010. "When does fractional Brownian motion not behave as a continuous function with bounded variation?," Statistics & Probability Letters, Elsevier, vol. 80(19-20), pages 1543-1550, October.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:19-20:p:1543-1550
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    References listed on IDEAS

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    1. Azmoodeh Ehsan & Mishura Yuliya & Valkeila Esko, 2009. "On hedging European options in geometric fractional Brownian motion market model," Statistics & Risk Modeling, De Gruyter, vol. 27(2), pages 129-144, December.
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