How countries and companies manage risks

Mathematical finance expert Abel Cadenillas explains the mathematics of risk management.

Katie Willis - 07 November 2017

In difficult economic times, mathematician Abel Cadenillas knows the best place for governments and industry to turn is to a mathematician. An expert in mathematical finance, Cadenillas has been using mathematics to answer the questions of economics and policy for more than 20 years. The answer, he says, lies in applying stochastic control.

"Stochastic control is the method of selecting the best policy when there is uncertainty within a system," Cadenillas explained. "This method has diverse applications, ranging from medicine to electrical engineering and everything in between."

Managing the risks

In terms of economics, Cadenillas is developing mathematical models that will allow governments and companies to better manage risk and identify optimal policies.

"Everybody does risk management every day when solving problems and making decisions under uncertain conditions," said Cadenillas. "The problem for governments is that there are many factors to consider in the decision making process. Our models will account for these factors, allowing leaders to make better, more informed decisions."

Personalized approach

Cadenillas is modeling and solving risk management problems in economics, finance, and insurance. The topics that he is investigating include optimal financial decisions under risk constraints, optimal debt ceiling for a country facing a debt crisis, optimal strategy to rescue a country facing a debt crisis, optimal government debt portfolio, and optimal government debt stabilization fund management. This research will be useful to reduce the chances of future financial crises and government debt crises, and to mitigate their negative effects.

To conduct this research, Cadenillas has recently been awarded an Insight Grant from the Social Science and Humanities Research Council (SSHRC). Cadenillas has worked in the area of mathematical finance for two decades. In 1996, in conjunction with Professor Emeritus Robert J. Elliott, Cadenillas started the University of Alberta's mathematical finance program. It is the oldest of its kind in Canada.