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

Financial institutions increasingly face risks where probabilities cannot be reliably estimated—including cyber risk, climate risk, operational risk, and model risk. Regulatory bodies such as the Basel Committee on Banking Supervision, the European Commission, and the UK’s Financial Conduct Authority have recognized this gap, calling for new approaches to manage non-probabilistic uncertainty. This paper develops a unified fuzzy utility framework for decision making under ambiguity, directly addressing this regulatory and practical need. We introduce fuzzy lotteries for modeling second-order uncertainty, fuzzy expected utility operators with a tunable parameter that captures the decision maker’s attitude toward ambiguity, a class of fuzzy measures that generalizes additive probabilities, fuzzy moments (variance, skewness, kurtosis) for asymmetric risk analysis, the fuzzy risk premium as a decision metric for resource allocation, and the Choquet and Sugeno integrals for ambiguity-averse behavior. As theoretical contributions, we prove three new theorems: fuzzy convergence to classical utility, bounds for the fuzzy risk premium based on higher-order moments, and the linear combination of risk aversion. We further introduce three practical extensions: regime-invariant decision structures, out-of-distribution stress-testing, and regime shift detection. All concepts are validated through comprehensive portfolio choice problems using empirical data from both the Tehran Stock Exchange and a developed global market, demonstrating the framework’s universal applicability. Practical implications for risk management professionals—including implementation steps and alignment with Basel Committee principles, Digital Operational Resilience Act requirements, and Financial Conduct Authority guidance—are discussed.