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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.

This paper analyzes a bivariate optimal dividend problem for an insurer with two collaborating business lines under a diffusion model with correlated Brownian motions. The framework incorporates dividend payouts, proportional reinsurance, and inter-line capital transfers to prevent bankruptcy. The authors provide complete analytical solutions, identifying three scenarios with closed-form value functions and optimal strategies. Results show a threshold dividend policy, with the more important line having a lower threshold. Optimal reinsurance decreases with aggregate reserves and stabilizes after a switching point. Correlation between lines affects reinsurance, and the capital transfer rule is consistent across scenarios.

The draft strengthens governance arrangements, clarifies management body roles, and enhances oversight of internal control, risk management, and compliance functions. It incorporates ICT and security risk management in line with DORA, requiring institutions to integrate digital operational resilience into governance frameworks. The revisions also address anti-money laundering, conflicts of interest, and gender-neutral remuneration. Stakeholders can submit feedback until October 2025, with final guidelines to replace the 2017 version.

This study explores how natural disasters challenge traditional risk management and insurance mechanisms. Researchers developed a three-strategy evolutionary game model to examine the competition among formal index insurance, informal risk sharing, and non-insurance. The model incorporates insurance company profits to aid optimal pricing. Findings suggest that basis risk and loss ratios strongly influence insurance adoption. Low basis risk and high loss ratios favor index insurance, while moderate loss ratios lead to informal risk sharing. Low loss ratios often result in no insurance uptake. Accurately estimating risk aversion and risk sharing ratios is essential for forecasting index insurance market trends.

This Final Report (EBA/RTS/2025/03) presents draft Regulatory Technical Standards (RTS) under the Capital Requirements Regulation (CRR) III. It addresses three mandates:
• An operational risk taxonomy with Level 1 event types, Level 2 categories and supplementary attributes (including ESG and ICT risks), to standardise how institutions classify loss events.
• Criteria for deeming the annual‑operational‑risk loss calculation “unduly burdensome” for certain institutions, allowing temporary waivers.
• Rules for adjusting loss‑data sets when firms merge or acquire entities, including currency conversion, re‑classification and fallback proxies.