Fuzzy utility framework tackles financial risks where probabilities fail

Financial institutions routinely face risks that resist the usual toolkit of probability estimates, from cyber attacks and climate hazards to operational failures and flaws in the models themselves. A new theoretical paper in Complex & Intelligent Systems, published as an open-access article on 26 October 2026, proposes a unified fuzzy utility framework for decision making under such ambiguity, where probabilities cannot be reliably estimated.

The framework, developed by Mehdi Shams, introduces several interconnected concepts. Fuzzy lotteries model second-order uncertainty, while fuzzy expected utility operators include a tunable parameter that captures a decision maker’s attitude toward ambiguity. A class of fuzzy measures generalizes additive probabilities, and fuzzy moments—variance, skewness and kurtosis—support analysis of asymmetric risk. The paper also defines a fuzzy risk premium as a decision metric for resource allocation and applies Choquet and Sugeno integrals to represent ambiguity-averse behavior.

Three new theorems form the theoretical core of the work. The first establishes fuzzy convergence to classical utility, showing how the fuzzy framework relates to standard expected utility theory. The second provides bounds for the fuzzy risk premium based on higher-order moments, and the third characterizes the linear combination of risk aversion. Together, these results aim to connect the fuzzy setting rigorously to established decision theory rather than treating it as a loose analogy.

Beyond the theorems, the author presents three practical extensions: regime-invariant decision structures, out-of-distribution stress-testing, and regime shift detection. These extensions are designed for portfolio choice problems, and the paper validates all concepts using empirical data from both the Tehran Stock Exchange and a developed global market, which the author presents as evidence of the framework’s applicability across different market environments.

The regulatory context motivates much of the work. The paper notes that the Basel Committee on Banking Supervision, the European Commission and the UK’s Financial Conduct Authority have recognized the gap in managing non-probabilistic uncertainty and have called for new approaches. The author discusses implementation steps for risk management professionals and alignment with Basel Committee principles, Digital Operational Resilience Act requirements and Financial Conduct Authority guidance.

As with any new theoretical framework, the results reported here are the author’s own mathematical proofs and portfolio demonstrations described in the paper; the article is an original research contribution rather than an independent evaluation of the framework’s performance in live institutional settings. Readers should also note that the published version is an early-release, peer-reviewed accepted manuscript that remains subject to further editorial edits before the final Version of Record appears. The framework’s long-term practical value for banks and insurers will depend on how its fuzzy measures, risk premium bounds and stress-testing tools perform once adopted beyond the validation datasets used in the paper.

Subject of Research: Fuzzy utility theory for decision making under ambiguity in financial risk management

Article Title: Advances in fuzzy utility theory for risk management: convergence, risk premium bounds, and aggregation of risk aversion

Article References: Shams, M. (2026). Advances in fuzzy utility theory for risk management: convergence, risk premium bounds, and aggregation of risk aversion. Complex & Intelligent Systems. https://doi.org/10.1007/s40747-026-02522-x

Image Credits: AI Generated

DOI: 10.1007/s40747-026-02522-x

Keywords: fuzzy utility theory, decision making under ambiguity, risk management, risk premium, Choquet integral, Sugeno integral, portfolio choice, second-order uncertainty, stress-testing, Basel Committee, financial regulation, ambiguity aversion