Predicting Extreme Events in Finance, Internet Traffic, and Weather

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Lecture Details

Date: 
2011
Location Information: 
CSS Webinar Series
Author: 
Mathukumalli Vidyasagar
Author Bio: 

Mathukumalli Vidyasagar was born in Guntur, India on September 29, 1947. He received the B.S., M.S. and Ph.D. degrees in electrical engineering from the University of Wisconsin in Madison, in 1965, 1967 and 1969 respectively. Between 1969 and 1989, he was a Professor of Electrical Engineering at various universities in the USA and Canada. His last overseas job was with the University of Waterloo, Waterloo, ON, Canada, where he served between 1980 and 1989. In 1989 he returned to India as the Director of the newly created Centre for Artificial Intelligence and Robotics (CAIR) in Bangalore, under the Ministry of Defence, Government of India. Between 1989 and 2000, he built up CAIR into a leading research laboratory with about 40 scientists and a total of about 85 persons, working in areas such as flight control, robotics, neural networks, and image processing. In 2000 he moved to the Indian private sector as an Executive Vice President of India's largest software company, Tata Consultancy Services. In the city of Hyderabad, he created the Advanced Technology Center, an industrial R&D laboratory of around 80 engineers, working in areas such as computational biology, quantitative finance, e-security, identity management, and open source software to support Indian languages. In 2009 he retired from TCS at the age of 62, and joined the Erik Jonsson School of Engineering & Computer Science at the University of Texas at Dallas, as a Cecil & Ida Green Professor of Systems Biology Science. In March 2010 he was named as the Founding Head of the newly created Bioengineering Department. His current research interests are in the application of stochastic processes and stochastic modeling to problems in computational biology, control systems and quantitative finance.

Abstract: 

As far back as 1963, Beniot Mandelbrot (who sadly passed away just a few weeks ago) pointed out that asset price movements in the real world don't follow the Gaussian distribution. Instead they are "heavy-tailed" -- that is, they display a kind of self-similarity and scale-invariance. Since then, similar patterns have been observed in extreme weather such as rainfall, and more recently, in Internet traffic. Recent research in "pure" probability theory shows that heavy-tailed random variables have some very unusual properties. For instance, if we average many observations of such variables, the averages move in a few large bursts instead of moving smoothly. Such behavior has indeed been observed in the stock market.

The pervasiveness of heavy-tailed distributions in so many diverse arenas has implications for modeling, and risk mitigation. How do we design Internet traffic networks and storage servers if the volume of traffic is heavy-tailed? How do we hedge our equity positions if asset prices move in a heavy-tailed manner?

In this talk I will describe the issues involved through a combination of intuitive arguments, visualizations, and formal mathematics. My hope is to inspire practicing engineers to become familiar with this fascinating class of models, and theoretical researchers to study the many open problems that still remain.

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