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Rohini Kumar: Small-time asymptotics for multi-scale stochastic systems and its applications in financial mathematics

Submitted by Andreas L. Freund on December 5, 2015 - 11:00am

Speaker: Rohini Kumar, Wayne State

Date: November 5, 2015

Title: Small-time asymptotics for multi-scale stochastic systems and its applications in financial mathematics

Abstract: We consider a system of fast-slow diffusions and study the tail probabilities of the slow process in small time. Obtaining small-time asymptotics of these tail probabilities is essentially a “large deviations” problem in probability theory and we obtain a “Large Deviations Principle” (LDP) for the slow process. The LDP is obtained by PDE techniques rather than probabilistic methods. Due to the mutli-scale nature of the problem, the PDE techniques involve averaging viscosity solutions of nonlinear PDEs. These results can be applied to pricing options close to maturity under fast mean-reverting stochastic volatility models.(This is joint work with Jean-Pierre Fouque, Jin Feng, Martin Forde and Lea Popovic.)

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