Exit Times and Extremes of Fractional Brownian motion and Spectrally Negative Levy Processes

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• Ceren Vardar Acar (Middle East Technical University)
• Monday 22 April 2024, 09:45-10:30
• External.

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TMLW02 - SGD: stability, momentum acceleration and heavy tails

Inspired by many applications, especially in Financial Mathematics and Heavy Tail Phenomena, this talk will begin with providing some old and improved bounds on the first hitting times of fractional Brownian motion and its draw-down process. Asymptotically, the tail of distribution of the first hitting time of drawdown/loss/regret process over [0, t] behaves like the tail of the marginal distribution at time t.  Next, our focus will be on the two-sided exit times of draw-down and draw-up processes of spectrally negative Levy processes. Finally, the Laplace transform of the “three-sided” exit times of spectrally negative Levy and its draw-down process from a rectangular region will be demostrated together with the Laplace transforms of these exit-times out of a Trapezoid.

This talk is part of the Isaac Newton Institute Seminar Series series.

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