The most popular and fundamental portfolio optimization problem is
Markowitz' / s one period mean-variance portfolio selection problem.
However, it is criticized because of its one period static nature.
Further, the estimation of the stock price expected return is a
particularly hard problem. For this purpose, there are a lot of
studies solving the mean-variance portfolio optimization problem
in continuous time. To solve the estimation problem of the stock
price expected return, in 1992, Black and Litterman proposed the
Bayesian asset allocation method in discrete time. Later on,
Lindberg has introduced a new way of parameterizing the price
dynamics in the standard Black-Scholes and solved the continuous
time mean-variance portfolio optimization problem.
In this thesis, firstly we take up the Lindberg' / s approach, we
generalize the results to a jump-diffusion market setting and we
correct the proof of the main result. Further, we demonstrate the
implications of the Lindberg parameterization for the stock price
drift vector in different market settings, we analyze the
dependence of the optimal portfolio from jump and diffusion risk,
and we indicate how to use the method.
Secondly, we present the Lagrangian function approach of Korn and
Trautmann and we derive some new results for this approach, in
particular explicit representations for the optimal portfolio
process. In addition, we present the L2-projection approach
of Schweizer for the continuous time mean-variance portfolio
optimization problem and derive the optimal portfolio and the
optimal wealth processes for this approach. While, deriving these
results as the underlying model, the market parameterization of
Lindberg is chosen.
Lastly, we compare these three different optimization frameworks
in detail and their attractive and not so attractive features are
highlighted by numerical examples.
| Identifer | oai:union.ndltd.org:METU/oai:etd.lib.metu.edu.tr:http://etd.lib.metu.edu.tr/upload/12613824/index.pdf |
| Date | 01 September 2011 |
| Creators | Sezgin Alp, Ozge |
| Contributors | Hayfavi, Azize |
| Publisher | METU |
| Source Sets | Middle East Technical Univ. |
| Language | English |
| Detected Language | English |
| Type | Ph.D. Thesis |
| Format | text/pdf |
| Rights | To liberate the content for public access |
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