Nos derniers articles

An agent with multiple loss models optimizes risk sharing with a counterparty using a mean-variance criterion adapted for ambiguity. Under a Cramér-Lundberg loss model, the optimal risk sharing contract and wealth process are characterized. The strategy is proven admissible, and the value function verified. The optimal strategy is applied to Spanish auto insurance data with differing models from cross-validation for numerical illustrations.

En 2024, la France vit plus que jamais dans une « société du risque» face aux tensions géopolitiques, au décrochage économique européen et à l'aggravation des risques climatiques (année la plus chaude, événements naturels coûteux). Les Français se sentent vulnérables et inquiets face aux risques de guerre et à la capacité future d'assurer les risques climatiques et autres. Le secteur de l'assurance, bien que créateur d'emplois et gérant un grand nombre de sinistres (dont le coût des événements naturels a atteint 5 milliards d'euros en France), fait face à une hausse de la sinistralité (dégâts des eaux, sinistres graves pour les professionnels, cyberattaques, sinistralité agricole record) et des coûts (réparation automobile, dépenses de santé).

The banking industry faces complex financial risks, including credit, market, and operational risks, requiring a clear understanding of the aggregate cost of risk. Advanced AI models complicate transparency, increasing the need for explainable AI (XAI). Understanding risk mathematics enhances predictability, financial management, and regulatory compliance in an evolving landscape.

This work presents a framework for constructing elicitable risk measures with properties like monotonicity, translation invariance, and convexity using multiplicative scoring functions. It defines necessary conditions for these properties and provides a method for developing new elicitable functionals, with applications in finance, statistics, and machine learning.

This paper examines the Solvency II correlation matrix used in Solvency Capital Requirement (SCR) calculations. It warns against misinterpreting null correlations as independence and highlights the matrix's limitations without a well-defined probabilistic model. It also critiques the flawed practice of arbitrarily increasing correlations to inflate capital requirements conservatively.

The paper explores Pareto optimality in decentralized peer-to-peer risk-sharing markets using robust distortion risk measures. It characterizes optimal risk allocations, influenced by agents' tail risk assessments. Using flood risk insurance as an example, the study compares decentralized and centralized market structures, highlighting benefits and drawbacks of decentralized insurance.

Elicitable functionals and consistent scoring functions aid in optimal forecasting but assume correct distributions, which is unrealistic. To address this, robust elicitable functionals account for small misspecifications using Kullback-Leibler divergence. These robust functionals maintain statistical properties and are applied in reinsurance and robust regression settings.

The RNN-HAR model, integrating Recurrent Neural Networks with the heterogeneous autoregressive (HAR) model, is proposed for Value at Risk (VaR) forecasting. It effectively captures long memory and non-linear dynamics. Empirical analysis from 2000 to 2022 shows RNN-HAR outperforms traditional HAR models in one-step-ahead VaR forecasting across 31 market indices.

This report uses UK fire statistics to model insurance claims for a company next year. It estimates the total sum of claims by modeling both the number and size of fires as random variables from statistical distributions. Monte Carlo simulations in R are used to predict the probability distribution of total claim costs.

"We study the general properties of robust convex risk measures as worst-case values under uncertainty on random variables. We establish general concrete results regarding convex conjugates and sub-differentials. We refine some results for closed forms of worstcase law invariant convex risk measures under two concrete cases of uncertainty sets for random variables: based on the first two moments and Wasserstein balls."