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This paper addresses the difficulty of 𝗶𝗻𝘁𝗲𝗴𝗿𝗮𝘁𝗶𝗻𝗴 𝗰𝗼𝗺𝗽𝗹𝗲𝘅, 𝗵𝗶𝗴𝗵-𝗱𝗶𝗺𝗲𝗻𝘀𝗶𝗼𝗻𝗮𝗹 𝘀𝗽𝗮𝘁𝗶𝗮𝗹 𝗱𝗮𝘁𝗮, 𝘀𝘂𝗰𝗵 𝗮𝘀 𝗰𝗹𝗶𝗺𝗮𝘁𝗲 𝗮𝗻𝗱 𝘀𝗮𝘁𝗲𝗹𝗹𝗶𝘁𝗲 𝗶𝗺𝗮𝗴𝗲𝗿𝘆, 𝗶𝗻𝘁𝗼 𝗽𝗿𝗲𝗱𝗶𝗰𝘁𝗶𝘃𝗲 𝗺𝗼𝗱𝗲𝗹𝘀 𝗳𝗼𝗿 𝗶𝗻𝘀𝘂𝗿𝗮𝗻𝗰𝗲.
The study proposes a novel multi-view contrastive learning framework designed to generate low-dimensional spatial embeddings. This method aligns data from multiple sources (e.g., satellite imagery and OpenStreetMap features) with coordinate-based encodings.
The resulting embeddings are shown to consistently improve predictive accuracy in risk models, demonstrated through a case study on French real estate prices. The paper highlights that the embeddings capture spatial structure, enhance model interpretability, and exhibit transferability to unobserved regions.

The paper argues that Shapley allocation is the most suitable risk allocation method for financial institutions, balancing theoretical properties, accuracy, and practicality. It overcomes perceived computational intractability by replacing the exponential analytical approach with an efficient Monte Carlo algorithm that scales linearly and becomes preferable for ≥10-14 units. The study proposes solutions for negative allocations, a consistent multi-level hierarchical framework (PTD, CTD, BU approaches), and demonstrates applicability to large trading portfolios under Basel 2.5 and FRTB regimes, showing Shapley better captures diversification and hedging effects compared to simpler methods.

The paper applies an extended mean-field game framework to model policyholder behavior in a large mutual insurance company, where surplus/deficit is shared among members. It proves global existence and uniqueness of the Nash equilibrium, characterized by constrained MF-FBSDEs, and solves these numerically using a modified deep BSDE algorithm. Key findings include: insurance demand rises with risk aversion, loss volatility, and surplus-sharing ratio; optimal coverage decreases toward the horizon; practical no-short-selling constraints reduce wealth disparities; and pool composition affects all members’ strategies through interdependence. Extensions to survival models and decentralized insurance are proposed.

Les simulations de Monte Carlo imbriquées exigées par Solvabilité II représentent un obstacle majeur à la rapidité du calcul du capital de solvabilité (SCR), limitant leur usage à des exercices de conformité ponctuels. Dans son article *“On the Estimation of Own Funds for Life Insurers”*, Mark-Oliver Wolf propose plusieurs avancées pour améliorer cette efficacité.

L’auteur démontre d’abord l’**équivalence entre les méthodes directe et indirecte** d’estimation du capital disponible : sous hypothèse d’absence d’arbitrage, elles convergent vers la même valeur. Cette propriété permet d’utiliser l’une pour valider l’autre, renforçant ainsi la fiabilité des modèles.

Wolf introduit ensuite une **famille d’“estimateurs mixtes”** généralisant ces approches. Tous partagent la même espérance, ouvrant la voie à l’usage de **variables de contrôle** permettant de réduire la variance sans introduire de biais. Deux variantes sont proposées :

* le **contrôle “crude”**, simple à implémenter, combine les estimateurs direct et indirect ;
* le **contrôle “mixed”**, plus avancé, exploite plusieurs estimateurs pour des gains supplémentaires.

Les tests sur trois modèles (MUST, IS, openIRM) montrent des **réductions de variance jusqu’à un facteur 10** dans les scénarios réalistes. L’efficacité dépend toutefois du degré de corrélation entre actifs et passifs, plus cette relation étant forte, plus les gains sont importants.

This document analyzes the impact of model uncertainty (ambiguity) on the insurance industry.
The study employed a 𝗿𝗼𝗯𝘂𝘀𝘁 𝗰𝗼𝗻𝘁𝗿𝗼𝗹 𝗳𝗿𝗮𝗺𝗲𝘄𝗼𝗿𝗸 that assumes insurers adopt strategies to maximize value against a "worst-case" scenario. The views expressed are that this leads to a new competitive market equilibrium characterized by:
• 𝗦𝗶𝗴𝗻𝗶𝗳𝗶𝗰𝗮𝗻𝘁𝗹𝘆 𝗵𝗶𝗴𝗵𝗲𝗿 𝗽𝗿𝗲𝗺𝗶𝘂𝗺𝘀 and 𝗶𝗻𝗰𝗿𝗲𝗮𝘀𝗲𝗱 𝗲𝗾𝘂𝗶𝘁𝘆 𝘃𝗮𝗹𝘂𝗮𝘁𝗶𝗼𝗻𝘀.
• 𝗠𝗼𝗿𝗲 𝗰𝗼𝗻𝘀𝗲𝗿𝘃𝗮𝘁𝗶𝘃𝗲 𝗹𝗶𝗾𝘂𝗶𝗱𝗶𝘁𝘆 𝗺𝗮𝗻𝗮𝗴𝗲𝗺𝗲𝗻𝘁, evidenced by higher precautionary reserves and delayed dividend payouts.
• 𝗦𝘂𝗯𝘀𝘁𝗮𝗻𝘁𝗶𝗮𝗹𝗹𝘆 𝗽𝗿𝗼𝗹𝗼𝗻𝗴𝗲𝗱 𝘂𝗻𝗱𝗲𝗿𝘄𝗿𝗶𝘁𝗶𝗻𝗴 𝗰𝘆𝗰𝗹𝗲, increasing in numerical simulations from 9.6 to 26 years.
• A long-run capacity distribution that is 𝗺𝗼𝗿𝗲 𝗰𝗼𝗻𝗰𝗲𝗻𝘁𝗿𝗮𝘁𝗲𝗱 𝗶𝗻 𝗹𝗼𝘄-𝗰𝗮𝗽𝗮𝗰𝗶𝘁𝘆 𝘀𝘁𝗮𝘁𝗲, implying slower recovery from adverse shocks.
The paper suggests these findings offer a theoretical explanation for the difficulty of detecting underwriting cycles in empirical data.

The provided text is an **academic article** that offers a comprehensive **analytical review of cyber risk management** within the insurance industry, focusing heavily on the **mathematical models** used for risk quantification and premium pricing. The review systematically covers the current state-of-the-art in cyber risk, discussing how dynamic and interconnected threats challenge traditional actuarial methods, necessitating the use of advanced quantitative tools like **stochastic models and copulas** to manage dependencies and calculate **Solvency Capital Requirements (SCR)**. It thoroughly details various **vulnerability functions** (including the well-known Gordon-Loeb model and its extensions) and different **premium calculation principles** (such as Expected Value and Mean-Variance), concluding that closer collaboration between different disciplines is essential for developing **robust cyber insurance and reinsurance solutions** in an increasingly digital landscape.

The geospatial Agent-Based Model (ABM) framework outlined in this article enables financial institutions, including insurers, to quantify direct and cascading climate risks, capturing spatial and temporal dynamics and supply chain disruptions overlooked by traditional models. It supports climate scenario analysis for enhanced risk assessment and portfolio management, revealing systemic risks affecting even indirectly exposed agents. The framework evaluates cost-effective adaptation strategies, showing how firms’ adaptive behaviors, like pre-emptive capital increases, reduce climate impacts. By integrating geospatial climate data with economic models, it bridges gaps between climate projections and financial decision-making, aiding risk management and capital allocation.

This research addresses the critical challenge of model ambiguity in insurance, where the true probabilities of losses are uncertain. It introduces randomly distorted Choquet integrals, a novel mathematical tool for creating flexible and dynamic risk measures. This provides a formal, unified methodology to resolve expert disagreements by extending industry-standard metrics like Value at Risk (VaR) and Average Value at Risk (AVaR). The framework allows a decision-maker to synthesize divergent opinions—whether on key parameters like a VaR confidence level or on the fundamental risk model itself (e.g., VaR vs. AVaR)—into a single, coherent, and scenario-dependent assessment.

The paper presents a dual-model framework for chaotic inference and rare-event detection. Model A, using Poincaré–Mahalanobis, focuses on geometric structure for stable inference. Model B, employing Correlation–Integral with Fibonacci diagnostics, emphasizes recurrence statistics and volatility clustering. The Lorenz–Lorenz experiments show that diagnostic weighting shifts inference from stability to rare-event focus. The Lorenz–Rössler experiments demonstrate Model B’s generalization across attractors, maintaining sensitivity to volatility. The framework combines stable geometric anchoring with robust rare-event detection, advancing systemic risk analysis. Future work aims to extend the models to higher-dimensional systems, optimize computational efficiency, and apply them to finance, climate, and infrastructure.

The study examines the relationship between ESG variables and financial risk, measured through logarithmic volatility. It introduces the Hierarchical Variable Selection (HVS) algorithm, designed for ESG datasets, which is reported to outperform aggregated ESG scores and traditional selection models by providing higher explanatory power with fewer variables. Findings suggest that ESG risk factors vary across sectors and between large- and small-cap firms, influenced by differences in regulation, expectations, and strategy. The authors highlight the robustness and adaptability of HVS, noting its effectiveness in identifying risk-relevant ESG variables across industries and its potential for broader applications in hierarchical datasets.