损失厌恶下的多期多目标不确定投资组合模型及算法

Multi-Period and Multi-Objective Uncertain Portfolio Selection Model under Loss Aversion and Its Algorithm

摘要: 金融市场具有复杂性和多态性，为了能够合理表达投资者所面临的主观不确定性，利用不确定变量刻画资产收益和风险的不确定特征，利用损失厌恶效用函数考虑投资者损失厌恶的心理，并同时考虑组合的流动性风险以及组合的多样性，构建损失厌恶下的多期多目标不确定投资组合模型。利用不确定理论，将不确定投资组合模型转换为确定型投资组合问题。由于所构建的投资组合模型是一个带约束的复杂非线性优化问题，传统的优化方法难以在有效的时间内得到模型的最优解。在已有的随机排序方法的基础上引入自适应机制，提出改进的粒子群算法。利用算例分析方法，检验改进粒子群算法的性能及投资组合模型在投资决策中的有效性。研究结果表明：改进的粒子群算法能够有效提高算法的求解精度，满足多期投资决策的要求；考虑损失厌恶下的多期多目标不确定投资组合模型能够反映不同投资者对投资目标的差异偏好。

Abstract: Real stock market is complex and polymorphic. To express investor’s subjective uncertainty reasonably, uncertain variable is used to describe the return and risk characteristic of asset. Furthermore, based on prospect theory, the loss-averse utility function is employed to portray investor’s loss aversion. Additionally, a multi-period and multi-objective uncertain portfolio model under loss aversion is proposed, in which the liquidity risk and diversification degree are also introduced. The uncertain portfolio model is transformed into a certain portfolio model based on uncertainty theory. Since the portfolio model is a complex nonlinear programming problem for which the traditional optimization methods may fail to obtain the optimal solution. To solve the portfolio model, an improved particle swarm optimization (IPSO) is also proposed. In IPSO, a self-adaptive stochastic ranking approach is employed, which is able to balance the abilities of exploration and exploitation as well as to balance the objective function value and the constraint violation function value for the PSO algorithm. A numerical experiment is presented to examine the effectiveness of IPSO algorithm and the portfolio model. The results show that IPSO is effective to solve the proposed model and the proposed portfolio model can express investor’s preference by adjusting the objective weights.