Mathematics and Financial Economics

, Volume 5, Issue 1, pp 29–46 | Cite as

On pricing and hedging in financial markets with long-range dependence

  • Alexander MelnikovEmail author
  • Yuliya Mishura


We study a mixed financial market with risky asset governed by both the standard Brownian motion and the fractional Brownian motion with Hurst index \({H\in(\frac12, 1)}\). We use representations of Hitsuda and Cheridito for the mixed Brownian and fractional Brownian process and present the solution of the problem of efficient hedging for \({H\in(\frac34, 1)}\). To solve the problem for \({H\in(\frac12, 1)}\) and to avoid some computational difficulties, we introduce the approximate incomplete semimartingale market, and the solution of the approximate problem of efficient hedging is considered. Then we pass to the limit and observe the asymptotic behavior of the solution of the efficient hedging problem.


Fractional Brownian motion Brownian motion Financial market Efficient hedging Minimal martingale measure 

JEL Classification

G11 G12 G13 

Mathematics Subject Classification (2000)

60G22 60J65 60H10 91G10 91G20 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada
  2. 2.Department of Probability, Statistics and Actuarial Mathematics, Mechanics and Mathematics FacultyKyiv Taras Shevchenko National UniversityKyivUkraine

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