Applications of Population Sampling to Ratemaking and Reserving in General Insurance:

How can insurers accurately estimate how much money to reserve for claims that haven’t been reported yet? And how can they fairly and efficiently price premiums for individual clients?

This PhD thesis in Statistics at the University of Toronto addresses two core challenges in general insurance using modern statistical approaches:

1. Reserving with population sampling:
   I propose a novel method based on statistical sampling theory to estimate the reserve needed for unreported claims. Instead of relying solely on classical actuarial models, I treat reported claims as a biased sample and use survival models (e.g., Cox regression) to estimate reporting probabilities—leading to more robust, semi-parametric reserve estimates.

2. Pricing with Bayesian statistics and surrogate models:
   In the context of auto insurance, I develop a Bayesian approach to pricing that incorporates both the insured’s individual characteristics and their claim history. To reduce the high computational cost of Bayesian inference, I introduce surrogate machine learning models that approximate outcomes efficiently, enabling faster, scalable pricing without compromising predictive power.