Abel Prize for Varadhan and Large Deviations in Finance

The award of the Abel Prize (often described as the Mathematics Nobel Prize) to Indian born mathematician Srinivasa S. R. Varadhan for his work on the theory of large deviations reminded me of the applications of this theory in finance. Basically one starts with a large and well diversified portfolio of securities and considers the probability distribution of large losses. If the underlying distributions have exponentially declining tails, then the theory of large deviations applies. The conditional probabilty distributions (conditioning on a large loss) can be computed in terms of the cumulant generating function and its Legendre transform.

At one time, this looked liked a very promising approach for risk modelling. Unfortunately, around this time, the mainstream risk management literature embraced fat tailed distributions with a vengeance. Once you bring in fat tails (which do not decline exponentially), the large deviations theory loses much of its applicability. However, there is no denying the mathematical elegance of the whole theory and as the Abel prize citation mentions, the theory has a wide range of applications in other fields.

Posted at 6:12 pm IST on Thu, 29 Mar 2007         permanent link

Categories: mathematics, statistics

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