具有灵活时间期限的混合投资组合优化模型

doi:10.16381/j.cnki.issn1003-207x.2021.0160

摘要/Abstract

摘要：

在经济全球化和金融一体化背景下，投资者资产配置需求变得越来越多元化。如何构建合理的多元化投资组合已成为金融理论研究的热点问题之一。为此，本文考虑由项目、股票及无风险资产组成的混合投资组合选择问题。假定在资产组合的投资期限由所选中项目执行期灵活确定的前提下，投资者同时考虑项目间依赖与排斥关系、交易成本及破产风险控制等现实因素，提出以终端财富净现值最大为目标的混合投资组合优化模型。然后，设计改进的多策略融合人工蜂群算法对所构建模型进行求解。最后，借助算例分析来阐明所提出模型的实用性及算法有效性。研究结果表明：灵活时间期限的混合投资组合策略较现有的灵活时间期限的项目投资组合策略更为有效。

关键词: 混合投资组合, 灵活时间期限, 人工蜂群算法, 现实因素

Abstract:

Under the background of economic globalization and financial integration， investors' asset allocation needs become more and more diversified. How to construct reasonable diversified portfolio strategy has become one of the hot issues in financial theory research. To this end， a mixed portfolio selection problem composed of project， stock and risk-free assets is considered. Assuming that the investment period of the portfolio is determined flexibly by the execution period of the selected project， the investors consider the real factors such as the dependence and exclusion relationship between the projects， the transaction cost and the bankruptcy risk control. A mixed portfolio optimization model with the objective of maximizing the net present value of terminal wealth is proposed. Then， an improved multi-strategy fusion artificial bee colony algorithm is designed to solve the proposed model. Finally， a numerical example is provided to illustrate the application of our model and demonstrate the effectiveness of the solution algorithm. The computational results show that the mixed portfolio investment strategy with flexible time horizon is more effective than the existing project portfolio investment strategy with flexible time horizon.

Key words: mixed portfolio, flexible time horizon, artificial bee colony algorithm, practical factors

中图分类号:

F830

刘勇军,伍健栋,张卫国. 具有灵活时间期限的混合投资组合优化模型[J]. 中国管理科学, 2024, 32(1): 23-30.

Yongjun Liu,Jiandong Wu,Weiguo Zhang. Mixed Portfolio Optimization Model Within Flexible Time Horizon[J]. Chinese Journal of Management Science, 2024, 32(1): 23-30.

图/表 5

表1

混合投资组合在时刻j结束投资的损益值αj"

$j$	3	4	5	6	7	8	9	10
$α j$	183	169	152	0	-177	-210	-249	-277

表1

表2

从时刻j开始投资的项目i在时刻h所需支付的执行成本及到期收益"

$i$	$ω i$	$c j i h$					$d j i h$	$i$	$ω i$	$c j i h$					$d j i h$
$i$	$ω i$	h=j	h=j+1	h=j+2	h=j+3	h=j+4	h=j+ωⁱ	$i$	$ω i$	h=j	h=j+1	h=j+2	h=j+3	h=j+4	h=j+ωⁱ
1	3	685.66	310.38	616.82	0	0	1543.08	11	5	754.32	459.62	345.23	450.35	356.99	3483.48
2	5	674.4	549.25	412.4	399.03	680.27	2854.27	12	5	714.34	323.45	613.14	573.79	709.64	3342.26
3	2	384.56	344.17	0	0	0	794.03	13	2	399.47	728.43	0	0	0	1111.82
4	5	642.68	776.7	301.97	556.1	706.31	3565.36	14	2	475.83	677.32	0	0	0	1284.17
5	3	606.26	660.88	445.94	0	0	1891.48	15	3	447.98	741.97	462.76	0	0	1521.14
6	2	758.89	657.29	0	0	0	1342.91	16	5	382.51	496.26	346.73	710.55	375.58	3139.04
7	5	571.27	371.09	486.67	637.07	520.92	2643.36	17	4	492.06	772.13	793.81	528.15	0	2457.53
8	2	517.01	608.88	0	0	0	1103.23	18	2	713.06	425.69	0	0	0	1171.53
9	3	556.57	625.2	600.52	0	0	1825.78	19	4	598.69	751.42	567.28	595.1	0	3069.58
10	2	702.61	560.82	0	0	0	1282.31	20	5	319.64	478.59	339.81	452.73	465.36	2279.02

表2

图1

表3

表4

不同模型下项目投资策略"

模型

项目启动时刻

j

T *

Δ W e

W T *

项

目1

项

目2

项

目3

项

目4

项

目5

项

目6

项

目7

项

目8

项

目9

项

目10

项

目11

项

目12

项

目13

项

目14

项

目15

项

目16

项

目17

项

目18

项

目19

项

目20

(P)

-913

10235.03

FTPP

-636

7854.57

表4

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第k期资产s	k = 1	k = 2	k = 3	k = 4	k = 5	k = 6	k = 7	k = 8	k = 9
s = 1	0.2831	0.2569	0.3501	0.2999	0.0000	0.0000	0.2438	0.2826	0.2725
s = 2	0.3318	0.2082	0.0000	0.0000	0.0000	0.3501	0.3491	0.3167	0.3292
s = 3	0.0000	0.0000	0.3501	0.3501	0.3501	0.0000	0.0000	0.0000	0.0000
s = 4	0.0782	0.2216	0.2999	0.0000	0.3501	0.3501	0.3499	0.3493	0.2964
s = 5	0.0000	0.0000	0.0000	0.3501	0.2999	0.2999	0.0573	0.0514	0.1019
s = 6	0.3069	0.3133	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000

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