Optimal allocation algorithm of financial re-sources based on return-risk equilibrium

Kai Dai; Yankui Xu

doi:10.3934/jimo.2025086

Article Contents

2025, Volume 21, Issue 7: 5093-5113. Doi: 10.3934/jimo.2025086

This issue Previous Article Price and quality optimization with the intertemporal reference price effect Next Article Linear fractional optimization for integer indefinite quadratic fractional problem

Optimal allocation algorithm of financial re-sources based on return-risk equilibrium

Kai Dai and
Yankui Xu^,

College of Innovation and Entrepreneurship, Pingdingshan University, Pingdingshan, 467000, China

^*Corresponding author: Yankui Xu
^*Corresponding author: Yankui Xu

Received: October 2024

Revised: April 2025

Early access: May 27, 2025

Published online: May 27, 2025

Abstract / Introduction Full Text(HTML) Figure(7) / Table(7) Related Papers Cited by

Abstract

To effectively balance the relationship between financial resource allocation, returns, and risks, a financial resource op-timization allocation method based on the Bayesian filtering algorithm is proposed. This method combines prior infor-mation and observed data to predict and update financial market risks through Bayesian filtering, thereby establishing a profit-risk balanced financial resource optimization allocation model. Utilizing fuzzy set theory, the multi-objective op-timization problem is transformed into a single-objective optimization problem, specifically maximizing the return-risk index. By employing an improved particle swarm optimization algorithm, the optimal allocation of financial resources and input ratios are determined. The research results demonstrate that within a risk division range of $ 3*10^{-5} $, this meth-od achieves maximized returns, effectively balancing returns and risks in financial resource allocation, validating its practicality and effectiveness.

Keywords:

Return-risk equilibrium,
financial resources,
optimal allocation,
risk prediction,
fuzzy set theory,
improved particle swarm optimization algorithm.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

Citation:

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Figure 1. Financial market risk prediction model based on Bayesian filtering

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Figure 2. The fitness value change curve of the improved particle swarm optimization algorithm before and after solving the problem

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Figure 3. Using Bayesian filtering algorithm for pre Sharp ratio

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Figure 4. Sharpe ratio after using Bayesian filtering algorithm

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Figure 5. Pareto efficiency test results of different methods under A1 project

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Figure 6. Pareto efficiency test results of different methods under A2 project

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Figure 7. Pareto efficiency test results of different methods under A3 project

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Table 1. Investment parameters of different property projects on Plot A-1

Type	Expected return	Standard deviation	Correlation coefficient
	Expected return	Standard deviation	Residence	Shops	Apartment	Villa
Residence	0.13	0.09	1
Shops	0.21	0.19	0.76	1
Apartment	0.19	0.19	0.91	0.81	1
Villa	0.26	0.33	0.86	0.76	0.81	1

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Table 2. Investment parameters of different property projects on Plot A-2

Type	Expected return	Standard deviation	Correlation coefficient
	Expected return	Standard deviation	Residence	Shops	Apartment	Villa
Residence	0.11	0.17	1
Shops	0.23	0.18	0.76	1
Apartment	0.26	0.16	0.91	0.81	1
Villa	0.31	0.29	0.86	0.76	0.81	1

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Table 3. Investment parameters of different property projects on Plot A-3

Type	Expected return	Standard deviation	Correlation coefficient
	Expected return	Standard deviation	Residence	Shops	Apartment	Villa
Residence	0.16	0.12	1
Shops	0.19	0.26	0.76	1
Apartment	0.21	0.17	0.91	0.81	1
Villa	0.26	0.31	0.86	0.76	0.81	1

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Table 4. Parameter settings for improved particle swarm optimization algorithm

Type	Numerical value
Population size	55
Maximum Number Of Iterations	255
Maximum inertia weight	0.9
Learning Factor 1	1.86
Learning Factor 2	2.1
What is maximum speed of a Particles	25
What is minimum speed of a Particles	-25

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Table 5. Comparison of financial resource optimization allocation performance of different methods

Method	Computational Complexity (Running Time/ms)	Time Complexity (Execution Time/ms)	Space Complexity (Memory Usage/MB)
Proposed Method	12.5	5.8	85
Chaos-based Financial Portfolio Selection Method	22.8	12.9	136
Online Deep Reinforcement Learning and Restricted Stacked Autoencoder-based Financial Portfolio Optimization Method	32.5	15.8	257
Z-number Theory and Fuzzy Neural Network-based Portfolio Selection Method	26.7	20.4	154
Financial Portfolio Optimization Method integrating Stochastic Programming and Financial Risk	19.8	18.8	167
Financial Portfolio Optimization Method based on Rank-dependent Utility	34.6	13.4	198
Scheduling Method based on Genetic Algorithm	25.8	10.2	110
Adaptive Fuzzy Model Predictive Control Method	28.7	12.7	128

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Table 6. Average Pareto efficiency values of different asset data

Asset Type	Average Pareto efficiency value	Standard deviation	Minimum value	Maximum value
Enterprise projects (A1-A3)	0.82	0.08	0.68	0.94
Stock	0.65	0.07	0.54	0.76
Treasury bond futures	0.50	0.06	0.42	0.58

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Table 7. Tukey's post inspection results

Asset Type	Mean difference	P-value	Significance
Enterprise projects vs stocks	+0.17	< 0.001	Yes
Enterprise project vs treasury bond futures	+0.32	< 0.001	Yes
Stock vs treasury bond bond futures	+0.15	< 0.001	Yes

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