﻿ 损失厌恶下的多期多目标不确定投资组合模型及算法

# 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

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.

1. 引言

2. 相关研究综述

3. 不确定理论预备知识

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4. 损失厌恶下的多期多目标不确定投资组合模型

：无风险资产在t时刻的财富；

：风险资产在t时刻的财富；

：无风险资产在t时刻的财富调整量；

：无风险资产在t时刻的财富调整量；

：无风险资产在第t期的收益率；

：风险资产在第t期的收益率；

：无风险资产在t时刻的非流动性指数；

：风险资产在t时刻的非流动性指数；

：风险资产在t时刻的交易费率；

：收益率的不确定分布；

：非流动性指数的不确定分布。

4.1. 问题描述

Figure 1. Schematic diagram of multi-period investment

4.2. 多期不确定投资组合

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1) 多期投资组合的目标函数

a) 损失厌恶效用

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b) 流动性风险

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c) 组合多样性

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2) 多期投资组合的约束条件

a) 安全性约束

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b) 自融资约束

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d) 权重约束

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3) 模型构建

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4.3. 增广加权Tchebycheff规划

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5. 改进的粒子群算法

5.1. 种群初始化

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5.2. 自适应随机排序方法

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Figure 2. Updating personal best

Figure 3. Updating global best

5.3. 种群速度和位置更新

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5.4. 算法流程

。若，则返回步骤3；否则，停止运算，并输出可行域内的全局极值。

6. 算例分析

Table 1. Uncertain return

Table 2. Uncertain illiquidity index

6.1. 改进的粒子群算法有效性检验

Table 3. Result comparison for algorithm

6.2. 多期投资组合策略

Table 4. Multi-period investment strategy (unit: million yuan)

Table 5. Objective values with different objective weights

7. 结束语

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