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Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert

Cite Score 2018: 0.85

SCImago Journal Rank (SJR) 2018: 0.354
Source Normalized Impact per Paper (SNIP) 2018: 0.604

Mathematical Citation Quotient (MCQ) 2017: 0.32

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Volume 26, Issue 2


Mean and covariance matrix adaptive estimation for a weakly stationary process. Application in stochastic optimization

Vincent Guigues
Published Online: 2009-09-25 | DOI: https://doi.org/10.1524/stnd.2008.0916


We introduce an adaptive algorithm to estimate the uncertain parameter of a stochastic optimization problem. The procedure estimates the one-step-ahead means, variances and covariances of a random process in a distribution-free and multidimensional framework when these means, variances and covariances are slowly varying on a given past interval. The quality of the approximate problem obtained when employing our estimation of the uncertain parameter is controlled in function of the number of components of the process and of the length of the largest past interval where the means, variances and covariances slowly vary. The procedure is finally applied to a portfolio selection model.

Keywords: adaptive estimation; weakly stationary process; stochastic optimization; value-at-risk; portfolio management

About the article

* Correspondence address: IMPA, Jardim Botanico, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, Brasilien,

Published Online: 2009-09-25

Published in Print: 2008-03-01

Citation Information: Statistics & Decisions International mathematical journal for stochastic methods and models, Volume 26, Issue 2, Pages 109–143, ISSN (Print) 0721-2631, DOI: https://doi.org/10.1524/stnd.2008.0916.

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