Mathematical analysis of the possibilistic mean – variance model

Abstract

The possibilistic mean – variance (MV) model enables the practitioners to model the imprecise probability and integrate their subjective judgements into the portfolio selection problem. Thus, it is a considerable alternative of the Markowitz’s traditional MV model. In this study, we analyze this model mathematically under the assumption that the possibility distributions of asset returns are given with the triangular fuzzy numbers. Within this scope, the portfolios which maximize the utility or performance are derived analytically. Furthermore, we illustrate the structure of its efficient frontier with examples.

Keywords

• Portfolio selection,possibility theory,triangular fuzzy numbers,, mean -variance model,efficient frontier,linear programming

Olabilirlik ortalama – varyans modelinin matematiksel analizi

Abstract

Olabilirlik ortalama – varyans (OV) modeli, kesin olmayan olasılığın modellenebilmesine ve kişisel yargıların ve beklentilerin portföy seçimi problemine entegre edilebilmesine imkan verir. Bu nedenle Markovitz’in geleneksel OV modelinin dikkate değer bir alternatifidir. Bu çalışmada varlık getirilerinin olabilirlik dağılımlarının üçgensel bulanık sayılar ile verildiği varsayımı altında bu modelin matematiksel analizi yapılmıştır. Bu kapsamda performansı ya da faydayı maksimum yapan portföyler analitik olarak elde edilmiştir. Ayrıca bu modelin verdiği etkin sınırın yapısı örnekler ile açıklanmıştır.

Keywords

• Portföy seçimi,olabilirlik teorisi,üçgensel bulanık sayılar,ortalama – varyans modeli,etkin sınır,lineer programlama

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