Prof. Jayanth R. Varma’s Financial Markets Blog

A blog on financial markets and their regulation

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.

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