Real-Time Bayesian Nonparametric Prediction of Solvency Risk
16 Pages Posted: 13 Jun 2017 Last revised: 10 Dec 2017
Date Written: December 8, 2017
Insurance regulation often dictates that insurers monitor their solvency risk in real time and take appropriate actions whenever the risk exceeds their tolerance level. Bayesian methods are appealing for prediction problems thanks to their ability to naturally incorporate both sample variability and parameter uncertainty into a predictive distribution. However, handling data arriving in real time requires a flexible nonparametric model, and the Monte Carlo methods necessary to evaluate the predictive distribution in such cases are not recursive and can be too expensive to rerun each time new data arrives. In this paper, we apply a recently-developed alternative perspective on Bayesian prediction based on copulas. This approach facilitates recursive Bayesian prediction without computing a posterior, allowing insurers to perform real time updating of risk measures to assess solvency risk, and providing them with a tool for carrying out dynamic risk management strategies in today's "big data"' era.
Keywords: density estimation; mixture model; nonparametric Bayes; risk management; value-at-risk; conditonal tail expectation.
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