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Permanent link (DOI): https://doi.org/10.7939/R36M33B8N

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Financial Model Estimation And Portfolio Rebalancing Open Access

Descriptions

Other title
Subject/Keyword
Portfolio Rebalancing, Fractional Brownian Motion
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Kang, Jiayin
Supervisor and department
Melnikov, Alexander (Mathematical and Statistical Science)
Examining committee member and department
Poutkaradze, Vakhtang (Mathematical and Statistical Science)
Melnikov, Alexander (Mathematical and Statistical Science)
Frei, Christoph (Mathematical and Statistical Science)
Cadenillas, Abel (Mathematical and Statistical Science)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematical Finance
Date accepted
2015-05-12T09:05:38Z
Graduation date
2015-11
Degree
Master of Science
Degree level
Master's
Abstract
In this thesis we organize the contents in three parts. The first part is about portfolio rebalancing with changing benchmarks and the second part is about modeling of fractional Brownian motion in financial market while the last part is the conclusion. In the first part, we introduce backgrounds in portfolio rebalancing and the rational why rebalancing is beneficial for a multi asset class portfolio. Then we describe four commonly used portfolio rebalancing methods and report other related comparisons. Then we introduce the proposed new portfolio rebalancing method and provide the back-testing results comparing with other methods using market data from June 2000 to July 2014 for a hypothetical multi-client institutional fund. In the second part we introduce the properties and results of the mixed Brownian and fractional Brownian process with Hurst parameter H: 3/4 < H < 1. Then we estimated Hurst parameter H for the Equity, Fixed Income, and Forex markets across all the countries to get an overall picture of the financial markets all over the world.
Language
English
DOI
doi:10.7939/R36M33B8N
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication
Melnikov & Mishura (2011): In the financial market, we assume is independent Brownian motion and is fractional Brownian motion with Hurst index H > 1/2. Then the financial market includes 2 assets: (1) non-risky asset: (2) risky asset governed by the linear combination of W and BH: Here: is the constant risk free rate. is the drift coefficient. is the volatility for the standard Brownian motion W. is the volatility for the fractional Brownian motion BH. Then the discounted price process has the form:Melnikov & Mishura (2011): 1. The mixed process where t is in [0, T] is equivalent in measure to a Brownian motion if and only if H is in (3/4, 1). 2. For H is in (3/4, 1), there exists a unique real-valued Volterra kernel such that (t is in [0, T]): 3. The representation below is unique: If is a Brownian motion on and is a real-valued Volterra Kernel such that 4. As a consequence of Property 3, the process is a semi-martingale with respect to its natural filtration. 5. Let Bt be a a Brownian motion on probability space and be a real-valued Volterra Kernel, . Then: 6. If we consider the following class of strategies and are , a.s., Then the discounted capital satisfies the condition a.s.

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