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 explores an insurance company managing financial risk through reinsurance, aiming to optimize terminal wealth and minimize ruin probability. Using neural networks, it finds the optimal reinsurance strategy based on expected utility and a modified Gerber-Shiu function, illustrated by a numerical example involving a Cramér-Lundberg surplus model.