Nos derniers articles

This paper provides a rigorous mathematical analysis of the axiomatic foundations used to quantify financial risk. The author traces the evolution of risk measurement from early standards like Value-at-Risk to more sophisticated frameworks including coherent, convex, and spectral risk measures. Central to the text are the representation theorems that define these measures through dual sets of probability scenarios and penalty functions. The scope extends to dynamic settings, where time-consistency is required for multi-period assessments, and systemic risk involving interconnected institutions. Finally, the research bridges the gap between theory and practice by integrating machine learning techniques, specifically examining the concentration of empirical estimators and the use of conformal prediction for distribution-free risk control.

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 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.

Bank regulators link capital to risk, but accurately measuring risk poses challenges. Banks use internal models, impacting Value-at-Risk (VaR) predictions and their exceedance frequency. Analyzing data, we find varied VaR and violations due to simulation methods, historical data, and holding periods. Banks’ modeling choices can reduce capital requirements strategically, potentially compromising the system's stability.

This paper introduces new characterizations for certain types of law-invariant star-shaped functionals, particularly those with stochastic dominance consistency. It establishes Kusuoka-type representations for these functionals, connecting them to Value-at-Risk and Expected Shortfall. The results are versatile and applicable in diverse financial, insurance, and probabilistic settings.