Browsing by Author "Ustun, Ozden"

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Citation - WoS: 31
Citation - Scopus: 38
Combined Forecasts in Portfolio Optimization: a Generalized Approach
(Pergamon-Elsevier Science Ltd, 2012) Ustun, Ozden; Kasimbeyli̇, Refail
In this paper a general mathematical model for portfolio selection problem is proposed. By considering a forecasting performance according to the distributional properties of residuals, we formulate an extended mean-variance-skewness model with 11 objective functions. Returns and return errors for each asset obtained using different forecasting techniques, are combined in optimal proportions so as to minimize the mean absolute forecast error. These proportions are then used in constructing six criteria related to the mean, variance and skewness of return forecasts of assets in the future and forecasting errors of returns of assets in the past. The obtained multi-objective model is scalarized by using the conic scalarization method which guarantees to find all non-dominated solutions by considering investor preferences in non-convex multi-objective problems. The obtained scalar problem is solved by utilizing F-MSG algorithm. The performance of the proposed approach is tested on a real case problem generated on the data derived from Istanbul Stock Exchange. The comparison is conducted with respect to different levels of investor preferences over return, variance, and skewness and obtained results are summarized. (C) 2010 Elsevier Ltd. All rights reserved.
Citation - WoS: 34
Citation - Scopus: 42
The Modified Subgradient Algorithm Based on Feasible Values
(Taylor & Francis Ltd, 2009) Kasimbeyli̇, Refail; Ustun, Ozden; Rubinov, Alex M.
In this article, we continue to study the modified subgradient (MSG) algorithm previously suggested by Gasimov for solving the sharp augmented Lagrangian dual problems. The most important features of this algorithm are those that guarantees a global optimum for a wide class of non-convex optimization problems, generates a strictly increasing sequence of dual values, a property which is not shared by the other subgradient methods and guarantees convergence. The main drawbacks of MSG algorithm, which are typical for many subgradient algorithms, are those that uses an unconstrained global minimum of the augmented Lagrangian function and requires knowing an approximate upper bound of the initial problem to update stepsize parameters. In this study we introduce a new algorithm based on the so-called feasible values and give convergence theorems. The new algorithm does not require to know the optimal value initially and seeks it iteratively beginning with an arbitrary number. It is not necessary to find a global minimum of the augmented Lagrangian for updating the stepsize parameters in the new algorithm. A collection of test problems are used to demonstrate the performance of the new algorithm.
Citation - WoS: 21
Citation - Scopus: 25
Multiobjective Programming and Multiattribute Utility Functions in Portfolio Optimization
(Infor, 2009) Ehrgott, Matthias; Waters, Chris; Kasimbeyli̇, Refail; Ustun, Ozden
In recent years portfolio optimization models that consider more criteria than the expected return and variance objectives of the Markowitz model have become popular. These models are harder to solve than the quadratic mean-variance problem. Two approaches to find a suitable portfolio for an investor are possible. In the multiattribute utility theory (MAUT) approach a utility function is constructed based on the investor's preferences and an optimization problem is solved to find a portfolio that maximizes the utility function. In the multiobjective programming (MOP) approach a set of efficient portfolios is computed by optimizing a scalarized objective function. The investor then chooses a portfolio from the efficient set according to his/her preferences. We outline these two approaches using the UTADIS method to construct a utility function and present numerical results for an example.