PORTFOLIO OPTIMIZATION IN STATISTICAL FINANCE
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Title
PORTFOLIO OPTIMIZATION IN STATISTICAL FINANCE
Author
Vancea , Adrian Petru
Advisors
Roy , Anindya
Program
Statistics
UMBC Department
Mathematics and Statistics
Document Type
thesis
Sponsors
University of Maryland , Baltimore County (UMBC)
Date Issued
2010-01-01
Abstract
In this thesis we will find the optimum portfolio for a given set of assets . Since the return is a random quantity we would like to maximize its expected value . Instead of assuming anything about the distribution of the assets , we will estimate the expected value of the return and maximize the estimator . This will be done using a predictive distribution of the assets based on their history . To find the predictive distribution we can use an ICA based model or a similar randomization scheme but we will not address the prediction problem in this thesis . We will invest in terms of probability . The constraints of the maximization problem will be that the probability of the return to be less than a given value $gamma$ not to fall below a given probability <italic>q<</> . We denote the probability of the return to be less than γ by <italic>F<sub>n+1,ω<</italic> . In the code for the brute force approach , which will give us the true value of the optimum portfolio and return , we will use a non-smooth approximation of <italic>F<sub>n+1,ω<</italic> . For the interior point method we will approximate <italic>F<sub>n+1,ω<</italic> by a smooth function <italic>tilde{F}<sub>ω<</italic> . We will do this by convoluting <italic>hat{F}<sub>ω<</italic> with the pdf of a normal distribution with zero mean and a very small variance . This approach is non-parametric , hence more robust . To solve the maximization problem we will apply a log-barrier method . We will give an interior point method and also a brute force approach which will solve the maximization problem . The brute force approach will be used only for the cases of <italic>k ≤ 3<</> assets . The role of the brute force approach will be mainly to give us the true solution to the maximization problem with which we will compare the solution given by the interior point method . In this way we will be able to validate the solution given by the interior point method for the cases of <italic>k ≤ 3<</> assets and to rely only on this method for the cases of <italic>k ≤ 4<</> assets .
Identifier
10340
Format
application:pdf
Language
en
Collection
UMBC Thesis and Dissertations
Rights Statement
This item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please see http://aok.lib.umbc.edu/specoll/repro.php or contact Special Collections at speccoll(at)umbc.edu.
Source
Vancea_umbc_0434M_10340.pdf
Access Rights
Access limited to the UMBC community. Item may possibly be obtained via Interlibrary Loan through a local library, pending author/copyright holder's permission.

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