Gibbs Posterior Inference on Value-at-Risk

13 Pages Posted: 20 Sep 2018

See all articles by Nicholas Syring

Nicholas Syring

Department of Mathematics

Liang Hong

The University of Texas at Dallas

Ryan Martin

North Carolina State University - Department of Statistics

Date Written: September 3, 2018

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.

Suggested Citation

Syring, Nicholas and Hong, Liang and Martin, Ryan, Gibbs Posterior Inference on Value-at-Risk (September 3, 2018). Available at SSRN: https://ssrn.com/abstract=3243531 or http://dx.doi.org/10.2139/ssrn.3243531

Nicholas Syring

Department of Mathematics ( email )

One Brookings Drive
Campus Box 1208
Saint Louis, MO MO 63130-4899
United States

Liang Hong (Contact Author)

The University of Texas at Dallas ( email )

2601 North Floyd Road
Richardson, TX 75083
United States

Ryan Martin

North Carolina State University - Department of Statistics ( email )

Raleigh, NC 27695-8203
United States

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