Penalized Regression and Lasso Credibility
by Thomas Holmes and Mattia Casotto
Predictive modeling plays a crucial role in the insurance industry, with generalized linear models (GLMs) commonly used for frequency, severity, and pure premium loss modeling. However, a key limitation of traditional GLMs is their inability to incorporate actuarial credibility effectively, as they assume full data credibility regardless of sample size. This can lead to suboptimal outcomes, especially for segments with limited data, as GLM estimates do not inherently adjust for volatility or lack of credibility.
To address this, the paper introduces penalized regression, specifically focusing on lasso penalization, as a solution to incorporate credibility within predictive models. Lasso regression functions as a "credibility-weighted" procedure, allowing actuaries to manage data constraints more effectively by reducing reliance on large data sets. The methodology aligns with Actuarial Standard of Practice No. 25 (ASOP 25) and requires a shift from traditional p-value analysis to a credibility-based interpretation of model coefficients.
This monograph explains the practical application of lasso credibility and how it helps assess both the significance and the magnitude of coefficients simultaneously, unlike GLMs, which focus solely on statistical significance. The discussion includes intuitive guidance for implementation, emphasizing the simplicity and robustness of tuning the penalty parameter over traditional p-value assessments.
Thomas Holmes is Akur8’s Chief Actuary for the US region and received his FCAS in 2019. He has experience with actuarial modeling for personal and commercial insurance, and is a frequent presenter at CAS events and Akur8 Academy webinars. Additionally, he volunteers with the CAS on predictive modeling topics and performs industry outreach to share actuarial modeling methodologies and best practices. Thomas holds music degrees from the University of Michigan and Ohio University, and enjoys playing the piano and writing music in his spare time.
Mattia Casotto is Akur8’s US Head of Product and Principal Scientist. He is the co-author of various works such as the research papers “Derivative Lasso” and “Credibility and Penalized Regression.” With more than nine years of experience in predictive modeling in insurance, Mattia was one of the original team members who started the pricing software Akur8. He holds two master’s degrees, one in Mathematics and one in Quantitative Finance, and has a passion for transparent machine learning and music.
