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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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2196-7040
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Volume 28, Issue 1

Issues

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

Abstract

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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Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
TOMMI SOTTINEN and LAURI VIITASAARI
International Journal of Theoretical and Applied Finance, 2018, Page 1850015
[2]
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Statistics & Probability Letters, 2017, Volume 130, Page 85

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