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.
The paper introduces a new approach to risk scaling, addressing challenges like limited data and heavy tails in risk assessment. It offers a robust, conservative method for estimating capital reserves, going beyond traditional scaling laws. The proposed framework improves long-term risk estimation, risk transfers, and backtesting performance, with empirical validation.
This study provides semi-explicit formulas for inf-convolution and optimal allocations, considering homogeneous, conditional, and absolutely continuous beliefs. The research also explores inf-convolution between Lambda value at risk and other risk measures, discussing optimal allocations and alternative Lambda value at risk definitions.
This paper defines vector-valued risk measures using axioms and shows they ignore dependence structures of input random vectors, unlike set-valued risk measures. Convex vector-valued risk measures are unsuitable for capital allocation in various financial applications, including systemic risk measures. The results also generalize to conditional settings.
This paper introduces a multivariate sparse multiscale Bernstein polynomial model for copula dependence structures, utilizing a Bayesian spike-and-slab prior. The method enhances efficiency by preserving significant components, reducing computational demands, and enabling practical applications in multivariate density estimation, particularly for financial risk forecasting.