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Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert

4 Issues per year

Cite Score 2017: 0.96

SCImago Journal Rank (SJR) 2017: 0.455
Source Normalized Impact per Paper (SNIP) 2017: 0.853

Mathematical Citation Quotient (MCQ) 2017: 0.32

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Volume 28, Issue 1


Robust replication in H-self-similar Gaussian market models under uncertainty

Pavel V. Gapeev / Tommi Sottinen / Esko Valkeila
Published Online: 2011-03-03 | DOI: https://doi.org/10.1524/stnd.2011.1074


We consider the robust hedging problem in the framework of model uncertainty, where the log-returns of the stock price are Gaussian and H-self-similar with H∈(1/2,1). These assumptions lead to two natural but mutually exclusive hypotheses, both being self-contained to fix the probabilistic model for the stock price. Namely, the investor may assume that either the market is efficient, that is the stock price process is a continuous semimartingale, or that the centred log-returns have stationary distributions. We show that to be able to super-hedge a European contingent claim with a convex payoff robustly, the investor must assume that the markets are efficient. If it turns out that the stationarity hypothesis is true, then the investor can actually super-hedge the option and thereby receive some net profit.

Keywords: robust replication; fractional Brownian motion; model uncertainty; arbitrage

About the article

* Correspondence address: Aalto University, Department of Mathematics and Systems Analysis, P.O. Box 11100, 00076 Aalto, Finnland,

Published Online: 2011-03-03

Published in Print: 2011-03-01

Citation Information: Statistics & Decisions International mathematical journal for stochastic methods and models, Volume 28, Issue 1, Pages 37–50, ISSN (Print) 0721-2631, DOI: https://doi.org/10.1524/stnd.2011.1074.

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