This thesis consists of two parts. The first part addresses the parameter estimation and calibration of the Generalized Hyperbolic (GH) distributions. In this part we review the classical expectation maximization (EM) algorithm and factor analysis for the GH distribution. We also propose a simple shrinkage estimator driven from the penalized maximum likelihood. In addition an on-line EM algorithm is implemented to the GH distribution; and its regret for general exponential family can be represented as a mixture of Kullback-Leibler divergence. We compute the Hellinger distance of the joint GH distribution to measure the performances of all the estimators numerically. Empirical studies for long-term and short-term predictions are also performed to evaluate the algorithms.
In the second part we applied the GH distribution to portfolio optimization and risk allocation. We show that the mean-risk portfolio optimization problem of a certain type of normal mixture distributions including the GH distribution can be reduced to a two dimensional problem by fixing the location parameter and the skewness parameter. In addition, we show that the efficient frontier of the mean-risk optimization problem can be extended to the three dimensional space. We also proposed a simple algorithm to deal with the transaction costs. The first and second derivatives of the CVaR are computed analytically when the underlying distribution is GH. With these results we are able to extend the effective number of bets (ENB) to general risk measures with the GH distribution. By diagonalizing the Hessian matrix of a risk measure we are able to extract locally independent marginal contributions to the risk. The minimal torsion approach can still be applied to get the local coordinators of the marginal contributions.
|Commitee:||Douady, Raphael, Rachev, Svetlozar, Xiao, Keli|
|School:||State University of New York at Stony Brook|
|Department:||Applied Mathematics and Statistics|
|School Location:||United States -- New York|
|Source:||DAI-B 78/03(E), Dissertation Abstracts International|
|Subjects:||Applied Mathematics, Finance|
|Keywords:||Cvar, Effective number of bets, Em algorithm, Factor analysis, Generalized hyperbolic distribution, Normal mixture distribution|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be