Professors Joe Gani and Chris Heyde and Their Contributions to Finance and Risk Management

This Perspective is dedicated to the memory of Professor Joseph Mark (Joe) Gani (1924–2016) and Professor Christopher Charles (Chris) Heyde (1939–2008), two scholars whose intellectual leadership profoundly shaped applied probability, mathematical statistics, and their interface with finance, insurance, and risk management. Their contributions extend beyond specific technical results to the development of research cultures grounded in probabilistic rigor, empirical relevance, and methodological transparency. We emphasize three enduring themes central to modern quantitative risk analysis. First, the systematic incorporation of heavy-tailed and non-Gaussian features in stochastic modeling, reflecting persistent empirical deviations from classical Gaussian assumptions in financial data. Second, the development of stochastic and time-series methodologies capable of handling dependence structures, including conditional heteroskedasticity and long-range dependence. Third, the principled integration of probabilistic modeling with data-driven and machine learning approaches, ensuring predictive performance is accompanied by interpretability and robustness. We situate these contributions within contemporary challenges in financial risk management, including systemic risk, environmental, social and governance (ESG) considerations, and climate finance. In particular, climate-related financial risks arise from both physical impacts (such as extreme weather events and long-term environmental change) and transition dynamics associated with the shift toward a low-carbon economy (including policy, technological, and market adjustments). These sources of risk introduce additional forms of dependence, nonlinearity, and model uncertainty, particularly in high-dimensional, data-rich settings. This Perspective highlights a forward-looking research agenda that preserves the foundational principles of applied probability while adapting them to modern financial systems characterized by real-time information flows and evolving risk structures. This legacy continues to shape how financial risk is modeled, measured, and understood in increasingly complex and interconnected environments.