Project With Himchan Jeong

Improving Efficiency of Algorithms for Calibrating Compound Risk Models with Random Effects

Any type of statistical inference using the method of maximum likelihood requires optimization. However, the most widely used optimization routines were originally designed for convex optimization problems and might end up at a local optimum when they are applied to highly non-convex objective functions such as the likelihood of a longitudinal model with random effects for claims. Therefore, we will (1) conduct a comprehensive empirical analysis to identify potential problems with the naïve application of optimization routines in non-Gaussian random effects models and (2) propose an EM algorithm that will be applied both for frequency and severity components so that we can calibrate a collective risk model with longitudinal data with more stability. The student will be mainly responsible for the first part, with the following objectives:

1. Familiarizing themselves with the current literature on compound risk models with random effects for posterior ratemaking.
2. Writing code to implement the simulation and identify problems with applying naïve optimization routines for calibrating a compound risk model with random effects.
3. Documenting all work.