Gibbs posterior inference on value-at-risk. Issue 7 (9th August 2019)

• Record Type: Journal Article
• Authors: Syring, Nicholas; Hong, Liang; Martin, Ryan
• Is Part Of: Scandinavian actuarial journal. Volume 2019:Issue 7(2019)
• Page Start: 548
• Page End: 557
• Publication Date: 2019-08-09
• Subjects: Direct posterior -- discrepancy function -- M-estimation -- model misspecification -- risk capital -- robust estimation; Insurance, Life -- Mathematics -- Periodicals; Insurance -- Mathematics -- Periodicals; 368.01
• DOI: 10.1080/03461238.2019.1573754
• Languages: English
• ISSNs: 0346-1238

Abstract

ABSTRACT: Accurate estimation of value-at-risk (VaR) and assessment of associated uncertainty is crucial for both insurers and regulators, particularly in Europe. Existing approaches link data and VaR indirectly by first linking data to the parameter of a probability model, and then expressing VaR as a function of that parameter. This indirect approach exposes the insurer to model misspecification bias or estimation inefficiency, depending on whether the parameter is finite- or infinite-dimensional. In this paper, we link data and VaR directly via what we call a discrepancy function, and this leads naturally to a Gibbs posterior distribution for VaR that does not suffer from the aforementioned biases and inefficiencies. Asymptotic consistency and root- n concentration rate of the Gibbs posterior are established, and simulations highlight its superior finite-sample performance compared to other approaches.