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 study introduces partial law invariance, a novel concept extending law-invariant risk measures in decision-making under uncertainty. It characterizes partially law-invariant coherent risk measures with a unique formula, deviating from classical approaches. Strong partial law invariance is introduced, proposing new risk measures like partial versions of Expected Shortfall for risk assessment under model uncertainty.