Effective a Posteriori Ratemaking with Large Insurance Portfolios via Surrogate Modeling

34 Pages Posted: 4 Dec 2022 Last revised: 25 Jul 2023

See all articles by Sebastian Calcetero Vanegas

Sebastian Calcetero Vanegas

University of Toronto

Andrei Badescu

University of Toronto - Department of Statistics

X. Sheldon Lin

Department of Statistical Sciences, University of Toronto

Date Written: November 12, 2022

Abstract

A posteriori ratemaking in insurance uses a Bayesian credibility model to upgrade the current premiums of a contract by taking into account policyholders' attributes and their claim history. Most data-driven models used for this task are mathematically intractable, and premiums must be then obtained through numerical methods such as simulation such MCMC. However, these methods can be computationally expensive and prohibitive for large portfolios when applied at the policyholder level. Additionally, these computations become "black-bo" procedures as there is no expression showing how the claim history of policyholders is used to upgrade their premiums. To address these challenges, this paper proposes the use of a surrogate modeling approach to inexpensively derive a closed-form expression for computing the Bayesian credibility premiums for any given model. As a part of the methodology, the paper introduces the "credibility index", which is a summary statistic of a policyholder's claim history that serves as the main input of the surrogate model and that is sufficient for several distribution families, including the exponential dispersion family. As a result, the computational burden of a posteriori ratemaking for large portfolios is therefore reduced through the direct evaluation of the closed-form expression, which additionally can provide a transparent and interpretable way of computing Bayesian premiums.

Keywords: Credibility, Ratemaking, Bayesian, Regression, Experience Rating

Suggested Citation

Calcetero-Vanegas, Sebastian and Badescu, Andrei and Lin, Xiaodong Sheldon, Effective a Posteriori Ratemaking with Large Insurance Portfolios via Surrogate Modeling (November 12, 2022). Available at SSRN: https://ssrn.com/abstract=4275353 or http://dx.doi.org/10.2139/ssrn.4275353

Sebastian Calcetero-Vanegas (Contact Author)

University of Toronto ( email )

105 St George Street
Toronto, Ontario M5S 3G8
Canada

Andrei Badescu

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

Xiaodong Sheldon Lin

Department of Statistical Sciences, University of Toronto ( email )

Department of Statistical Sciences
100 St George Street
Toronto, Ontario M5S 3G3
Canada

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

Paper statistics

Downloads
61
Abstract Views
296
Rank
643,596
PlumX Metrics