| The investors always look forward to finding an investment choice with the maximum investment return and minimum investment risk among various assets.This kind of portfolio optimization problem was proposed by Markowitz(1952),in which the expected return and risk were expressed by the expected value and variance,respectively.Since then,numerous researchers have been working on the portfolio models and solving algorithms.As we all know,the complexity of the financial systems inevitably leads to the uncertain information and random information simultaneously.In situations where historical data is missing or invalid,relying on subjective estimates from experts is more convincing than using probability theory.Therefore,this thesis assumes the return rate of asset securities as an uncertain random variable,and studies the portfolio optimization problem taking into account downside risk and higher moments under the uncertain random environment.The main research work of this paper as follows:(1)We present an uncertain random bi-objective mean-variance-VaR-entropy model for portfolio selection problem by considering downside risks and diversification constraints.Here,investment return and risk are,respectively,quantified by uncertain random expected value and variance.Then,the formulated uncertain random model is transformed into two equivalent deterministic models.(2)We define the concept of kurtosis for uncertain random variable based on the chance theory and derive the deterministic expressions of kurtosis under three kinds of distributions(linear distribution,zigzag distribution and normal distribution).Then,an uncertain random mean-variance-skewness-kurtosis-entropy model is formulated for portfolio optimization problem,and the equivalent deterministic model under zigzag distribution is derived.(3)We use the second generation of fast non-dominated sorting genetic algorithm with elite strategy(NSGA-Ⅱ algorithm)to solve the equivalent bi-objective model,and propose a new optimal solution criterion to find a single optimal solution suitable for investor preference in the Pareto optimal solution set.Finally,a numerical simulation is carried out to verify the practicability of the model and the effectiveness of the algorithm.Finally,we give a summary of this article and further research prospects. |
