Application of Hidden Markov Model to Auto Telematics Data and the Effect of Universal Demand Law Change on Corporate Risk Taking in the U.S. Property & Casualty Insurance Industry

Abstract

There are two themes in this dissertation, that is, the effect of universal demand law change on corporate risk-taking in the U.S. property & casualty insurance industry, and the application of hidden Markov model to auto telematics data. The first chapter presents my study in the first theme and the rest two chapters present the other theme. In Chapter 1, "Does Shareholder Litigation Affect Corporate Risk-Taking? Evidence from the Property-Casualty Insurance Industry", I explore whether shareholder litigation affects corporate risk-taking differently depending on distinct organizational structures. I use a law change, called Universal Demand (UD) Law, as an exogenous shock and develop three risk-taking measures that are unique in the U.S. property-casualty insurance industry: leverage risk, asset risk, and underwriting risk. The insurance industry provides an interesting opportunity for the study as shareholders in mutual insurers are an ambiguous concept in the legal world, as opposed to the common argument in the insurance literature. The results show that along with UD law adoption, insurers increase their risk-taking. After taking organizational structures into account, the impact of the law change differentiates. Stock insurers increase all three risk-taking measures while mutual insurers decrease their Leverage Risk and increase Asset Risk measures. For different time windows, stock insurers respond faster with respect to their Asset Risk compared to mutual insurers. In addition, I proceed to examine the main economic channel for the impact and find that the free cash flow argument is not the main channel. Chapters 2 and 3 present the study in auto telematics data using a proprietary data source. Both studies are based on the application of hidden Markov model (HMM). Specifically, Chapter 2, "Auto Insurance Pricing Using Telematics Data: Application of a Hidden Markov Model", develops an HMM-based clustering framework to predict auto insurance losses using driving characteristics extracted from telematics data. Through a simulation experiment based on a proprietary telematics data set, I show that HMM can effectively classify driving trips using model-implied hidden states, and HMM-based pricing methods provide better predictive power measured by both deviance statistics and mean squared error. Importantly, the proposed framework not only enables us to price usage-based insurances at a granular level, but it is also viable for estimating long-term insurance losses utilizing the limiting properties of HMM. Chapter 3, "Theoretical Framework of a 3-Layer Hidden Markov Model for Auto Insurance Pricing", is a theoretical extension of the second chapter to improve the framework at a more granular level. I develop a 3-layer HMM for risk classification, which links driving behavior characteristics with risk classes and loss estimation. The proposed model presents a direct structure among all variables and utilizes time series data without aggregation. Furthermore, this study provides a theoretical framework to estimate the 3-layer HMM using the Expectation-Maximization (EM) algorithm. The parameters of Bernoulli distributed loss count (per unit of time) and Gamma distributed loss severity can be solved at least numerically, and the negative definite Hessian matrix indicates that the solution of the first-order condition of the log-likelihood function achieves its local maximum.