Gibbs posterior inference on value-at-risk |
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Authors: | Nicholas Syring Ryan Martin |
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Institution: | 1. Postdoctoral Lecturer in Statistics, Department of Mathematics, Washington University, Washington, MO, USA;2. Associate Professor in the Department of Statistics, North Carolina State University, Raleigh, NC, USA |
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Abstract: | ABSTRACTAccurate 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. |
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Keywords: | Direct posterior discrepancy function M-estimation model misspecification risk capital robust estimation |
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