Robust Versions of the Lower and Upper Possibilistic Mean - Variance Models for the One Period or Two Periods Cases

Abstract

It is easy to use possibility theory in modeling incomplete information. Robust optimization is an important tool when there is parameter uncertainty. Thus, in this study, we propose robust versions of the lower and upper possibilistic mean - variance (MV) models when there are multiple possibility distribution scenarios. Here, we use entropy as a diversification constraint. In addition, we reduce these robust versions to concave maximization problems. Furthermore, we generalize them for two periods portfolio selection problem by using fuzzy addition and multiplication. On the other hand, these generalizations are not concave maximization problems. Finally, we give an illustrative example by using different solvers in Gams modeling system.

Keywords

• Entropy
• Fuzzy Arithmetic
• Portfolio Selection
• Possibility Theory
• Robust Optimization

Bir ya da İki Periyotlu Durumlar için Alt ve Üst Olabilirlik Ortalama - Varyans Modellerinin Dayanıklı Versiyonları

Abstract

Tam olmayan bilgiyi modellemede olabilirlik teorisini kullanmak kolaydır. Parametre belirsizliği olduğunda dayanıklı optimizasyon önemli bir araçtır. Bu nedenle bu çalışmada, birden çok olabilirlik dağılımı senaryosu olduğunda alt ve üst olabilirlik ortalama - varyans (OV) modellerinin dayanıklı versiyonları önerilmiştir. Burada entropi çeşitlendirme kısıdı olarak kullanılmıştır. Bununla birlikte bu dayanıklı versiyonlar konkav maksimizasyon problemlerine indirgenmiştir. Üstelik bunlar, iki periyotlu portföy seçimi problemine bulanık toplama ve çarpma kullanılarak genelleştirilmiştir. Öte yandan bu genelleştirmeler, konkav maksimizasyon problemleri değildir. Son olarak, Gams modelleme sisteminde farklı çözücüler kullanılarak açıklayıcı bir örnek verilmiştir.

Keywords

• Entropi
• Bulanık Aritmetik
• Portföy Seçimi
• Olabilirlik Teorisi
• Dayanıklı Optimizasyon

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