Asymptotic properties of certainty equivalent measures of risk for extreme risks

Description

We study a general representation of convex or coherent risk measures known as certainty equivalent measures of risk, first introduced by Vinel and Krokhmal (2017). This framework enables the direct incorporation of risk preferences-grounded in the utility theory of von Neumann and Morgenstern (1944)-into convex or coherent risk measures by constructing such measures as infimal convolutions of certainty equivalents. We derive first- and second-order asymptotic expansions for the certainty equivalent measure of risk. Building on the first-order expansion, we propose estimation methods for intermediate and extreme risk levels. Using techniques from extreme value theory, we establish asymptotic normality. Simulation studies and a real-data application are conducted to evaluate the performance of the proposed estimators.

Period	29 Jun 2026 → 30 Jul 2026
Event title	The 29th International Congress on Insurance: Mathematics and Economics
Event type	Conference
Location	Seoul, Korea, Republic ofShow on map