Erik Baurdoux (LSE) - Lp optimal prediction of the last zero of a spectrally negative Lévy process
|Starts:||14:00 14 Nov 2019|
|Ends:||15:00 14 Nov 2019|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
Erick Baurdoux joins us for the Probability seminar.
Given a spectrally negative Lévy process $X$ drifting to infinity, we are interested in finding a stopping time which minimises the $L^p$ distance with the last zero of $X$.
We prove that solving this optimal prediction problem is equivalent to solving an optimal stopping problem in terms of a two dimensional strong Markov process involving the duration of the excursion of $X$ away from the negative half line.
We show that an optimal stopping time is given by the first time that $X$ exceeds a boundary depending on the time spent above the level zero.
Role: Associate Professor in Statistics
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