Fuzzy Portfolio Selection Based On Credibility Theory

The investment portfolio theory is the core content of modern financial area. The most important problem it faced is how to deal with the uncertainty. The classical models and methods regards uncertainty as randomness. However, with the rise of the study of behavioral finance, the fuzziness in the security market gradually attracts more and more attentions. In traditional fuzzy theory, the biggest weakness is the lack of the mathematical foundations, and that limited the fuzzy uncertainty study.Credibility theory is a developed a theory recently, it created by professor Liu Baoding of Tsinghua University. Credibility theory created a completely and rigorously axiomatic system like the probability theory, and push the study of the fuzzy theory.Fuzzy portfolio selection based on credibility theory is the study of how to measure the uncertainty investment income and risk, and then establishment of various optimization model on the basis of investors’ risk consciousness difference, at last, design of effective algorithm. Based on credibility theory framework, the paper establish the portfolio selection fuzzy model. And the paper introduced the the three classic index, Jansen index, Sharp index and the Treynor index which traditionally used for the measurement of fund performance, used to model for portfolio optimization. This article first introduces the absolute deviation, semi absolute deviation risk value and credibility risk measure. On this basis, the use of fuzzy programming method based on mean absolute deviation model, credibility value at risk model return risk models, especially the establishment of credibility measure of mean model. And for the first time using a sharp index on portfolio effectiveness measure. By combing fuzzy simulation and genetic algorithm, hybrid intelligent algorithms are designed to solve those models which cannot be converted into the deterministic equivalent forms.