Weighted Automata and Regular Expressions for Financial Systems

TL;DR

This paper introduces a formal framework using weighted automata and regular expressions for modeling, analyzing, and optimizing financial systems with uncertain variables.

Contribution

It develops weighted finance automata and regular expressions, establishing their correspondence and providing algorithms for decision and optimization problems.

Findings

Established a Kleene-Schützenberger-type correspondence.

Developed translation procedures between formalisms.

Analyzed decision and optimization problems for WFFAs.

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-Sch\"utzenberger-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.