نوع مقاله : مقاله انگلیسی برای ویژه‌نامه "تغییر اقلیم و صنعت بیمه"

نویسنده

• Mohammad Reyhani

Deputy Head of Life Insurance Department, Taavon Insurance Co.

چکیده

BACKGROUND AND OBJECTIVES: The increasing frequency of hydro-meteorological events, particularly floods driven by climate change, presents a significant challenge to the global insurance industry. Traditional actuarial models, which rely on the assumption of stationarity, are failing to capture the non-linear and spatially interconnected nature of modern flood risks. This failure results in premium mispricing and a widening "protection gap," particularly in developing nations. In response, the industry has turned towards Deep Learning (DL) models like Convolutional Neural Networks (CNNs). While offering predictive power, these models suffer from two critical flaws hindering their operational deployment. First, they are "data-hungry," requiring vast historical datasets that are non-existent in "data-scarce markets" like Iran, where historical loss records are often fragmented or non-digital. Second, their "black-box" nature violates stringent regulatory transparency requirements, such as those of the Central Insurance of Iran (Bimeh Markazi), which demand explicable premiums. This study addresses these gaps by designing and validating "PICA" (Physics-Informed and Causally-Aware), a novel conceptual framework for flood risk pricing. The specific objectives are to: (1) Design the PICA framework by synthesizing state-of-the-art AI components including Graph Neural Networks (GNNs) and Physics-Informed Neural Networks (PINNs); (2) Overcome data scarcity by embedding hydrodynamic laws (Shallow Water Equations) directly into the model's loss function; (3) Ensure regulatory compliance by integrating causal inference constraints to prioritize physical risk drivers over spurious correlations; and (4) Empirically validate PICA against benchmarks under simulated data-scarce conditions relevant to the Iranian context.
METHODS: To achieve these objectives, a multi-phase mixed-methods design was employed. Phase 1 involved a PRISMA 2020 systematic review of Scopus, Web of Science, and IEEE Xplore (2020-2025), synthesizing 52 elite articles to identify gaps in hybrid AI modeling and inform the architectural design of PICA. Phase 2 focused on quantitative validation using a high-fidelity synthetic dataset. Due to the lack of consistent real-world data, a "ground truth" environment was generated using the industry-standard HEC-RAS 2D hydrodynamic model. This simulation modeled 50 distinct flood events over a complex 100km² virtual urban watershed with 10,000 assets, providing precise values for water depth, velocity, and financial loss. The PICA framework was architected as a Hybrid Graph Neural Network (GNN), where the watershed topology was represented as a graph to capture water flow between hydrological units. The model was trained using a composite loss function that penalized prediction error, violations of physical laws (Mass and Momentum conservation), and causal structure violations. The framework was compared against two robust benchmarks: a 2D-CNN and a Random Forest (RF) regressor. All models were evaluated under two scenarios: a "Data-Rich" scenario (using 100% of the dataset) and a critical "Data-Scarce" scenario (using only 20% of the data) to simulate the Iranian market conditions. Performance was evaluated using Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and the Diebold-Mariano (DM) test. Additionally, SHAP analysis assessed explainability, and sensitivity analysis on hyperparameters confirmed stability.
FINDINGS: Phase 1 confirmed that no existing framework successfully integrates GNNs, PINNs, and Causal ML for actuarial pricing. Quantitative results in Phase 2 demonstrated the profound impact of physics-informed regularization. In the "Data-Rich" scenario, PICA (RMSE = 0.119) modestly outperformed the 2D-CNN (RMSE = 0.137) and Random Forest (RMSE = 0.141), indicating that with abundant data, pure DL models are competitive. However, in the critical "Data-Scarce" scenario, the benchmarks collapsed; the CNN’s RMSE deteriorated by over 250% to 0.482, and the Random Forest to 0.530, exhibiting severe overfitting. In stark contrast, PICA leveraged its physics-informed constraints to maintain robust accuracy, achieving an RMSE of 0.165. This represents a 65.8% reduction in prediction error compared to the CNN in data-scarce conditions. The Diebold-Mariano test confirmed this performance gap was statistically significant (p < 0.001). Furthermore, SHAP analysis revealed a crucial distinction in logic: PICA consistently prioritized valid physical drivers like "Maximum Water Depth," whereas CNNs relied on spurious "spatial coordinates" , indicating they were learning artifacts rather than causation. Finally, sensitivity analysis confirmed the model's robustness, demonstrating stable performance across a wide range of physics weights (0.1 ≤ ≤ 1), ensuring that reliance on physics did not lead to underfitting.
CONCLUSION: This research validates PICA as a transformative solution for flood risk pricing in data-scarce markets. The findings provide definitive empirical evidence that "teaching" deep learning models underlying physical laws effectively substitutes for missing historical data, acting as a universal prior for accurate generalization. For the Iranian market, these implications are significant. PICA offers the Central Insurance of Iran and private insurers a viable pathway to leapfrog the "data gap" in high-risk basins like Karun and Karkheh. It enables the immediate development of high-resolution, regulator-compliant pricing models without waiting decades for data accumulation. Specifically, the framework supports "Parametric Insurance" products, triggered by physics-verified metrics rather than manual adjustments. Future research should focus on bridging the "Sim-to-Real" gap by applying Transfer Learning strategies to fine-tune this physics-based framework on real-world claims data, operationalizing the model for national deployment.

کلیدواژه‌ها

• Actuarial Modeling
• Causal Inference
• Flood Risk
• Graph Neural Networks
• Hybrid Deep Learning
• Physics-Informed Neural Networks

عنوان مقاله [English]

A Physics-Informed and Causally-Aware (PICA) Conceptual Framework for Flood Risk Pricing: A Hybrid Deep Learning Approach for Data-Scarce Insurance Markets

نویسنده [English]

• Mohammad Reyhani

Deputy Head of Life Insurance Department, Taavon Insurance Co.

چکیده [English]

The escalating frequency and severity of hydro-meteorological events, particularly floods driven by climate change, present a profound systemic challenge to the global insurance and reinsurance industry. Traditional actuarial pricing models, predominantly based on Generalized Linear Models (GLMs) and historical loss tables, rely on the fundamental assumption of risk stationarity. This assumption has been rendered obsolete by the rapidly changing climate, making legacy models increasingly incapable of capturing the complex, non-linear, and spatially-interconnected nature of modern flood risk. In response to these limitations, standard data-driven Deep Learning (DL) models, such as Convolutional Neural Networks (CNNs), have been proposed as superior alternatives for risk forecasting. However, despite their theoretical promise, these models suffer from two critical flaws that strictly hinder their operational adoption in real-world insurance underwriting. First, they are notoriously "data-hungry," requiring massive, high-resolution datasets of historical losses to generalize effectively. Such datasets are unavailable in most "data-scarce markets," including Iran and much of the Global South, leading to poor model generalization and high predictive uncertainty. Second, their "black-box" nature is fundamentally incompatible with the stringent regulatory and fiduciary requirements of the insurance industry, which demands model transparency, fairness, and explainability (XAI) for pricing decisions. A model that cannot causally explain why it assigns a high premium to a specific property is operationally and ethically unusable. This study addresses this critical research and implementation gap. The primary objective is to design and validate a novel conceptual framework, "PICA" (Physics-Informed and Causally-Aware), for flood risk pricing. This study aims to achieve four specific goals: (1) To formally design the PICA framework by synthesizing state-of-the-art components from diverse AI fields; (2) To specifically address the data-scarcity problem by embedding hydrodynamic physical laws directly into the model’s learning process (Physics-Informed); (3) To resolve the "black-box" problem by integrating causal inference techniques to ensure model outputs are explainable and aligned with real-world causality (Causally-Aware); and (4) To empirically validate the performance of the PICA framework against benchmark DL models, particularly under simulated data-scarce conditions. In this study we used a rigorous multi-phase, mixed-methods research design, combining a systematic review with a high-fidelity quantitative simulation. The first phase, Framework Development, utilized a systematic review following the PRISMA 2020 protocol. Data sources included Scopus, Web of Science, and IEEE Xplore (2020–2025). The analysis focused on "architectural synthesis" of 52 elite articles covering Physics-Informed Neural Networks (PINNs), Graph Neural Networks (GNNs), and Causal Machine Learning. This synthesis directly informed the novel mathematical design of the PICA framework. The second phase, Framework Validation, consisted of a quantitative simulation experiment to test the hypothesis under controlled conditions. A high-fidelity synthetic dataset was generated using the HEC-RAS 2D hydrodynamic model, simulating 50 distinct stochastic flood events over a virtual 100-square-kilometer urban watershed containing 10,000 unique property assets. The primary material was the PICA framework itself, architected as a Hybrid Graph Neural Network (GNN) to explicitly capture the network topology of flood propagation. Two benchmark models were constructed for comparison: (1) a state-of-the-art 2D-Convolutional Neural Network (CNN) and (2) a baseline Random Forest (RF) model. The experimental procedure involved training all models under two distinct scenarios: a "Data-Rich" scenario (using 100% of simulated loss data) and a "Data-Scarce" scenario (using only 20% of available data). Predictive accuracy was evaluated using Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE), with statistical significance determined by the Diebold-Mariano (DM) test. Additionally, Shapley Additive Explanations (SHAP) analysis was conducted to validate model explainability. The Phase 1 review confirmed that while GNNs, PINNs, and Causal ML are individually established, no existing framework integrates all three for actuarial pricing. This led to the formalization of PICA's novel composite loss function: L_total=L_data+λ_phys*L_phys+λ_causal*L_causal. Here, L_phys penalizes violations of the Shallow Water Equations, and L_causal penalizes violations of a predefined causal graph. In Phase 2 validation, quantitative results were significant. In the "Data-Rich" scenario, the PICA framework (RMSE = 0.119) modestly outperformed the CNN (RMSE = 0.137). However, the critical finding emerged in the "Data-Scarce" scenario. The performance of the data-hungry benchmarks collapsed, with the CNN's RMSE deteriorating to 0.482. In stark contrast, the PICA framework leveraged its physics-informed component to maintain robust accuracy (RMSE = 0.165). This represents a 65.8% reduction in prediction error compared to the standard CNN in data-scarce conditions. The Diebold-Mariano test confirmed this superiority was statistically significant (p<0.001). Furthermore, SHAP analysis revealed that PICA correctly identified 'Water Depth' and 'Flow Velocity' as primary risk drivers, whereas the CNN relied on spurious spatial artifacts, confirming PICA effectively resolves the black-box problem. This research successfully validates the PICA framework, demonstrating that the strategic synthesis of physics-informed, causally-aware, and graph-based deep learning provides a superior solution for flood risk pricing in data-scarce markets. The findings provide definitive proof that "teaching" a model the underlying physics of a peril can effectively substitute for the lack of historical data.

کلیدواژه‌ها [English]

• Actuarial Modeling
• Causal Inference
• Flood Risk
• Graph Neural Networks
• Hybrid Deep Learning
• Physics-Informed Neural Networks