Probability maximization models for portfolio selection under ambiguity |
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Authors: | Takashi Hasuike Hiroaki Ishii |
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Institution: | (1) Department of Information and Physical Sciences, Graduate School of Information Science and Technology, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan |
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Abstract: | This paper considers several probability maximization models for multi-scenario portfolio selection problems in the case that
future returns in possible scenarios are multi-dimensional random variables. In order to consider occurrence probabilities
and decision makers’ predictions with respect to all scenarios, a portfolio selection problem setting a weight with flexibility
to each scenario is proposed. Furthermore, by introducing aspiration levels to occurrence probabilities or future target profit
and maximizing the minimum aspiration level, a robust portfolio selection problem is considered. Since these problems are
formulated as stochastic programming problems due to the inclusion of random variables, they are transformed into deterministic
equivalent problems introducing chance constraints based on the stochastic programming approach. Then, using a relation between
the variance and absolute deviation of random variables, our proposed models are transformed into linear programming problems
and efficient solution methods are developed to obtain the global optimal solution. Furthermore, a numerical example of a
portfolio selection problem is provided to compare our proposed models with the basic model. |
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Keywords: | Portfolio selection problem Stochastic programming Probability maximization model Multi-scenario model |
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