Fat-Tailed Regression Modeling with Spliced Distributions

27 Pages Posted: 18 Sep 2017

See all articles by Guojun Gan

Guojun Gan

University of Connecticut

Emiliano A. Valdez

University of Connecticut - Department of Mathematics

Date Written: September 14, 2017

Abstract

Insurance claims data usually contains a large number of zeros and exhibits fat-tail behavior. Misestimation of one end of the tail impacts the other end of the tail of the claims distribution; such can affect both the adequacy of premiums and needed reserves to hold. In addition, insured policyholders in a portfolio are naturally non-homogeneous. It is an ongoing challenge for actuaries to be able to build a predictive model that will simultaneously capture these peculiar characteristics of claims data and policyholder heterogeneity. Such models can help make improved predictions and thereby ease the decision making process. This paper proposes the use of spliced regression models for fitting insurance loss data. A primary advantage of spliced distributions is its flexibility to accommodate modeling different segments of the claims distribution with different parametric models. The threshold that breaks the segments is assumed to be a parameter and this presents an additional challenge in the estimation. Our simulation study demonstrates the effectiveness of using multi-stage optimization for likelihood inference and at the same time, the repercussions of model misspecification. For purposes of illustration, we consider three-component spliced regression models: the first component contains zeros, the second component models the middle segment of the loss data, and the third component models the tail segment of the loss data. We calibrate these proposed models and evaluate their performance using a Singapore auto insurance claims dataset. The estimation results show that the spliced regression model performs better than the Tweedie regression model in terms of tail fitting and prediction accuracy.

Keywords: Frequency-Severity Models, Spliced Distributions, Tweedie Distributions, Heterogeneity, Multi-Stage Optimization

JEL Classification: C10, C13, G22

Suggested Citation

Gan, Guojun and Valdez, Emiliano A., Fat-Tailed Regression Modeling with Spliced Distributions (September 14, 2017). Available at SSRN: https://ssrn.com/abstract=3037062 or http://dx.doi.org/10.2139/ssrn.3037062

Guojun Gan

University of Connecticut ( email )

341 Mansfield Rd, U-1009
Storrs, CT 06269-1009
United States

Emiliano A. Valdez (Contact Author)

University of Connecticut - Department of Mathematics ( email )

341 Mansfield Road U-1009
Storrs, CT 06269-1009
United States

HOME PAGE: http://www.math.uconn.edu/~valdez

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
107
Abstract Views
615
Rank
456,834
PlumX Metrics