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Gord Willmot

Munich Re Chair in Insurance
Professor, Graduate Officer (Actuarial Science)

Department of Statistics and Actuarial Science
University of Waterloo
Waterloo, Ontario
CANADA N2L 3G1

(519) 888-4567, ext. 36594
Fax: (519) 746-1875

E-mail:
Office: M3 4006

Research and Scholarly 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. (Professional Activities, Graduate Student Supervision and Degrees)

Recent Publications

  • Cai, J., Feng, R., and Willmot, G.E. The compound Poisson surplus model with interest and liquid reserves: Analysis of the Gerber-Shiu discounted penalty function, 23 pages, Methodology and Computing in Applied Probability, to appear.
  • Landriault, D. and Willmot, G.E. On the Gerber-Shiu discounted penalty function in the Sparre Anderson model with an arbitrary interclaim time distribution, 16 pages, Insurance: Mathematics and Economics, to appear.
  • Willmot, G.E. and Woo, J.K. On the class of Erlang mixtures with risk theoretic applications, North American Actuarial Journal, 2007, 2, 99-115. Discussion, 2007, 2, 115-117. Authors’ reply, 2007, 2, 117-118.(more)

Biography

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 9th 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.


Last Modified:  Monday 25 July 2011
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