Real-time Bayesian non-parametric prediction of solvency risk

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 non-parametric 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.