Stochastic models for risk and queueing applications

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In attempting to analyze insurance losses arising in connection with health coverages as well as property and casualty insurance situations involving homeowner and automobile coverages, it is imperative to understand that a portfolio of insurance business is very complicated in terms of the nature of its past and future risk-based behaviour. There are various deterministic and stochastic influences at play, and the precise prediction of the future claims experience necessitates that all such influences and their effects be identified. The role of probability and statistics is vitally important in assessing whether a quantitative (i.e., theoretical) model is able to accurately predict the claims experience of a portfolio of insurance business. Probability and statistics also play a crucial role in terms of analyzing congestion in waiting lines or queues, which frequently occur in many facets of everyday life. For example, we all typically experience some amount of waiting in common places such as the supermarket, the bank, and the doctor's office. The study of queueing theory, a branch of applied probability, provides the essential mathematical framework that decision makers need in order to efficiently streamline processes to remove/reduce any bottlenecks which may arise in settings such as hospital emergency rooms and computer network systems. In this proposal, it is my goal to develop mathematically tractable results, in conjunction with effective computational procedures, pertaining to a variety of stochastic models arising in both insurance risk and queueing applications. It is expected that the results from this proposed research will prove useful in adding to the current state of knowledge concerning these kinds of stochastic models, and perhaps more importantly, stimulate further ideas for investigation with a view towards more precisely reflecting real-world conditions.