Abstract

The emergence of the worldwide SARS epidemic in 2003 led to a revived interest in the study of infectious diseases. Mathematical models have become important tools in analyzing transmission dynamics and measuring effectiveness of controlling strategies. In hope of further applying them to design insurance coverage against infectious diseases, the author makes an attempt to build a bridge between epidemiological modelling and actuarial mathematics. Based on classical compartment models of ordinary differential equation systems, the first part of this thesis is devoted to developing insurance policies among susceptible and infected participants and then formulating their financial obligations using actuarial notation. For the purpose of practical applications, the thesis employs a variety of parameter estimation techniques and numerical methods of calculating premiums and reserves. The theory is later demonstrated to design insurance products for the Great Plague in Eyam and the SARS Epidemic in Hong Kong. In the second part, the thesis also investigates a stochastic model by incorporating the theory of comonotonicity and copulas. The idea of approximating a random vector indicating infectivity levels is developed by two approaches. While one is to find its closest conditional random vector in stochastic orders, the other examines the dependency structure of its component variables through copulas and then constructs a new random vector by transforming uniform random variables