Weighted Automata and Regular Expressions for Financial Systems

2026-04-19

AI Summary

This work addresses the formal modeling and efficient analysis of quantitative properties in financial systems driven by uncertain economic variables. It introduces Weighted Finite Financial Automata (WFFA) and Weighted Financial Regular Expressions, establishing a scenario-based, compositional language-theoretic framework. For the first time in financial contexts, the study formulates a Kleene–Schützenberger correspondence between weighted automata and regular expressions and designs a declarative specification language that supports effective translation between them. The proposed approach enables computable analysis of extreme payoffs for financial instruments and trading strategies, identifies expressive yet computationally tractable subclasses, and facilitates efficient formal verification across multi-market scenarios.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

We introduce weighted finite finance automata (WFFA), a formal framework for modeling and analyzing quantitative properties of financial systems driven by uncertain economic variables such as stock prices, interest rates, and exchange rates. The model provides a compositional and language-theoretic approach to scenario-based financial analysis, enabling systematic evaluation of financial instruments and trading strategies. To specify such systems, we introduce weighted finance regular expressions, a declarative language for quantitative financial properties. We establish a Kleene-Schützenberger-type correspondence between WFFAs and weighted finance regular expressions, together with effective translation procedures between the two formalisms. On the algorithmic side, we investigate fundamental decision and optimization problems for WFFAs, including the computation of extremal payoffs, and identify expressive yet computationally tractable subclasses. These results provide a foundation for formal, compositional, and efficient analysis of financial systems under multiple market scenarios.

Problem

• weighted automata
• financial systems
• regular expressions
• quantitative analysis
• uncertain economic variables

Innovation

• weighted finite finance automata
• weighted finance regular expressions
• Kleene-Schützenberger correspondence
• compositional financial modeling
• extremal payoff computation