Actuarial models and their Bayesian analysis

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The summer of 2013 marked Canada with a number of high profile tragedies and disasters including: the Alberta floods, and the flooding of significant parts of downtown Calgary; the tanker train explosion in Lac Megantic; the 100-year storm and flooding in parts of Toronto and surrounding areas. As tragic as these incidents were, their impact on the majority of surviving affected individuals and businesses in Canada would have been even worse were it not for the protection afforded by insurance models and insurance policies designed by actuarial scientists.**The main thrust of my research program is to develop new Bayesian statistical models and / or methods for use in contexts of interest to actuarial scientists and actuarial practitioners in industry; in particular, in non-life / property and casualty insurance settings. A Bayesian statistical method treats all unknowns appearing in a model as random quantities and derives their distribution given the known information. Bayesian methods have a long history of successful application in actuarial science and have many desirable properties. For example, they allow past experience or prior evidence to be incorporated into a model and yield results that are easily understood. **Non-life insurance claims are often a mix of some very small, many mid-sized, and some extremely large values. Standard distributions (e.g., lognormal, exponential, Pareto, Weibull) often provide a poor overall fit to such a collection of claim values. One objective of my research program is to continue my work on developing more appropriate distributional models for these settings, explore modified versions of these models (e.g., truncated versions appropriate for use when insurance claims are known to be capped), explore various extensions of them to multivariate settings, and explore implementations of these models using Bayesian methods. Improved models for individual claim sizes will enable actuarial scientists and practitioners to more effectively price individual insurance policies.**An insurer will often manage one or more lines of insurance containing many thousands or even millions of policies. For a given line, an insurer must forecast the aggregate amount (called the claim or loss reserve) representing the money that should be held by the insurer in order to be able to pay all future claims arising from policies currently in force and policies written in the past. A special case is when a when a line of insurance consists of several correlated subportfolios, and this enormously complicates the matter of determining the overall loss reserve. Another objective of my research program is to develop better loss reserve forecasting models.**Appropriate and fair insurance premiums and the sound capitalization of insurance companies should matter and be a concern to most members of our society. My research program addresses these topics. It will also develop new statistical models and methods that are likely to find application in a variety of fields including actuarial science, risk management, survival analysis, and reliability engineering.