Hua-Chen New Theory of Economic Optimization

2025-04-27

AI Summary

This paper addresses fundamental challenges in economic optimization theory—including system stability assessment, uniqueness verification of equilibria, and structural dynamic optimization—by proposing a novel stochastic modeling paradigm grounded in Markov chains. Methodologically, it integrates stochastic process analysis with structural matrix theory to introduce the “economic structural matrix invariant” (Chen’s invariant), enabling a quantifiable, programmable, and AI-implementable economic optimization framework. Unlike conventional mathematical economics and mainstream equilibrium approaches, the framework abandons deterministic assumptions, supporting stability testing, corporate bankruptcy prediction, product-category ranking, macroeconomic trend forecasting and policy intervention, and structural optimization decisions. Empirical validation confirms both theoretical rigor and engineering feasibility, offering a new computational tool for intelligent economic governance.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Equilibrium
• Search and Optimization: Other Foundations of Search & Optimization

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Between 1957-1985, Chinese mathematician Loo-Keng Hua pioneered economic optimization theory through three key contributions: establishing economic stability's fundamental theorem, proving the uniqueness of equilibrium solutions in economic systems, and developing a consumption-integrated model 50 days before his death. Since 1988, Mu-Fa Chen has been working on Hua's theory. He introduced stochastics, namely Markov chains, to economic optimization theory. He updated and developed Hua's model and came up with a new model (Chen's model) which has become the starting point of a new economic optimization theory. Chen's theory can be applied to economic stability test, bankruptcy prediction, product ranking and classification, economic prediction and adjustment, economic structure optimization. Chen's theory can also provide efficient algorithms that are programmable and intelligent. {Stochastics} is the cornerstone of Chen's theory. There is no overlap between Chen's theory, and the existing mathematical economy theory and the economics developments that were awarded Nobel Prizes in Economics between 1969 and 2024. The distinguished features of Chen's theory from the existing theories are quantitative, calculable, predictable, optimizable, programmable and can be intelligent. This survey provides a theoretical overview of the newly published monograph cite{5rw24}. Specifically, the invariant of the economic structure matrix, also known as the Chen's invariant, was first published in this survey.

Problem

• Develops a new economic optimization theory using stochastics and Markov chains.
• Provides quantitative, calculable, and programmable solutions for economic stability.
• Introduces Chen's invariant for economic structure optimization and prediction.

Innovation

• Integrated stochastic methods like Markov chains
• Developed programmable, intelligent economic algorithms
• Introduced quantifiable Chen's invariant for optimization