报告题目：Mixture of Experts Regression Models for Property and Casualty Insurance
报告人：X. Sheldon Lin (Department of Statistical Sciences, University of Toronto)
Sheldon Lin, PhD, ASA, ACIA, is currently a Professor of Actuarial Science in the Department of Statistical Sciences at the University of Toronto. He has published extensively in the area of insurance risk modelling and management and has authored/co-authored more than 60 refereed research papers and two books. He is an Editor for Insurance: Mathematics and Economics, a top research journal in actuarial science. For details, visit http://www.utstat.utoronto.ca/~sheldon/cv.pdf
Understanding the effect of policyholders' risk profile on the number and the amount of claims, as well as the dependence among different types of claims, are critical to insurance ratemaking and IBNR-type reserving. To accurately quantify such relations, it is essential to develop a regression model which is flexible, interpretable and statistically tractable.
In this presentation, I will discuss a highly flexible nonlinear regression model we have recently developed, namely the logit-weighted reduced mixture of experts (LRMoE) models, for multivariate claim frequencies or severities distributions. The LRMoE model is interpretable as it has two components: Gating functions to classify policyholders into various latent sub-classes and Expert functions to govern the distributional properties of the claims. The model is also flexible to fit any types of claim data accurately and hence minimize the issue of model selection.
Model implementation is illustrated with a simulation study and two real data applications. The first application involves fitting the multivariate claim frequency data from a European P&C insurer. The model enables us to interpret the fitting in an insurance perspective and to visualize the relationship between policyholders' information and their risk level, as well as the usefulness for insurance ratemaking. The second application deals with insurance loss severity data that exhibits heavy-tail behavior. We show that our model is applicable to fit the severity and reporting delay components of the dataset, which is useful and crucial for an adequate prediction of IBNR reserve.