**Munich Re Chair in Insurance**

**Contact Information:**

Gord Willmot

## Research interests

Professor Willmot's research interests involve the analysis of insurance losses, with particular emphasis on the theory and application of aggregate claims models and models for the insurer's surplus associated with a particular block of insurance business. His main approaches to the study of these models involves a variety of analytical tools, including those from applied probability and mathematical reliability theory.

The main event which is of interest in connection with the insurer's surplus is referred to as ruin, i.e., the surplus becomes negative. Related quantities of interest include the time of ruin, the surplus immediately prior to the ruin-causing event, and the deficit at the time of ruin. These quantities are of much interest in connection with financial risk management by the insurer, and a unified treatment is available via the so-called discounted penalty function.

In the analysis of standard models for the insurer's surplus, the discounted penalty function typically satisfies an integral equation that may be analyzed via a variety of different approaches. Techniques from renewal theory, Laplace transforms, and other areas of applied probability have been utilized by Professor Willmot and his collaborators to obtain information about the distributions and moments of these quantities of interest.

The distribution of the time of ruin, also of interest in a queueing theoretic context, has been the subject of recent study, and the approach Professor Willmot has employed has involved Laplace transform inversion. The derivation of the moments of the time of ruin was carried out through the use of a combination of Laplace transform techniques and normalized stop-loss moments, which are also of interest in connection with mathematical reliability theory. Similar techniques have also been used in the analysis of the deficit.

The normalized stop-loss moment approach referred to above has also been used by Professor Willmot in a more direct context to analyze the moments of the amount payable by the re-insurer under a stop-loss insurance agreement. These results are particularly well suited for use in connection with the so-called phase-type class of probability distributions, which have their origins in queueing theory and are well suited for computational implementation.

## Education/biography

- 1980 BMath (honours co-op) University of Waterloo
- 1981 MMath University of Waterloo
- 1986 PhD University of Waterloo
- 1989 F.S.A. Fellow of the Society of Actuaries
- 1989 F.C.I.A. Fellow of the Canadian Institute of Actuaries

Professor Willmot is the Munich Re Professor of Insurance at Waterloo, and is an adjunct professor at the University of Toronto. He is a Fellow of the Society of Actuaries and a Fellow of the Canadian Institute of Actuaries. He is a co-author of the textbook entitled *Loss Models*, which is required reading for two of the professional actuarial examinations of the Society of Actuaries. Recently, he was invited to teach a short course on his research and related topics at the Nineth International Congress on Insurance: Mathematics and Economics, at Laval University in Quebec City in July 2005. At the same congress, he was a keynote speaker on aggregate claims models. He also taught an intensive seminar on risk theory for the Society of Actuaries for several years.

## Selected publications

- Willmot, G.E., and Woo, J.K. On the analysis of a general class of dependent risk precesses. Insurance: Mathematics and Economics, 2012, 51, 134-141.
- Willmot, G.E. On mixing, compounding, and tail properties of a class of claim number distributions, Scandinavian Actuarial Journal, 2011, 21 pages, forthcoming article.
- Cai, J., Fang, Y., Li, Z., and Willmot, G.E., Optimal reciprocal reinsurance treaties under the joint survival probability and the joint profitable probability, Journal of Risk and Insurance, 2011, 24 pages, to appear.
- Landriault, D., Shi, T., and Willmot, G.E. Joint densities involving the time of ruin in the Sparre Andersen risk model under exponential assumptions. Insurance: Mathematics and Economics, 2011, 49, 371-379.
- Cheung, E.C.K., Landriault, D., Willmot, G.E., and Woo, J.K. On orderings and bounds in a generalized Sparre Andersen risk model. Applied Stochastic Models in Business and Industry, 2011, 27, 51-60.
- Willmot, G.E., and Lin, X.S. Risk modelling with the mixed Erlang distribution, Applied Stochastic Models in Business and Industry. 2011, 27, 2-16. Discussion 2011, 27, 17-22.
- Kim, S.Y., and Willmot, G.E. The proper distribution of the deficit in the delayed renewal risk model. Scandinavian Actuarial Journal, 2011, 118-137.
- Willmot, G.E. Distributional analysis of a generalization of the Polya process. Insurance: Mathematics and Economics, 2010, 47, 423-427.
- Willmot, G.E., andWoo, J.K. Surplus analysis for a class of Coxian interclaim time distributions with applications to mixed Erlang claim amounts. Insurance: Mathematics and Economics, 2010, 46, 32-41.
- Cheung, E.C.K., Landriault, D., Willmot, G.E., andWoo, J.K. Structural properties of Gerber-Shiu functions in dependent Sparre Andersen models. Insurance: Mathematics and Economics, 2010, 46, 117-126.