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Colloquium: Some Examples of Skorokhod Embeddings and Their Applications
Start Date: 2/19/2014Start Time: 3:00 PM
End Date: 2/19/2014End Time: 4:00 PM

Event Description
Ju-Yi Yen, assistant professor, University of Cincinnati


Abstract: Given a target probability measure μ, the Skorokhod embedding problem consists of finding a stopping time τ of Brownian motion (Bt)t≥0 such that Bt^τ is a uniformly integrable martingale; and Bτ has the given law μ. Conversely, Skorokhod embedding is often used to construct, or rather embed martingales in Brownian motion. There exist many solutions to Skorokhod embedding with target measure μ. We take advantage of the explicit character of the Azema-Yor (Skorokhod embedding) algorithm, to describe precisely some remarkable and simple examples of these martingales. We also show that the Brownian excursion theory allows one to solve the Skorokhod embedding problem. In doing so, we consider more general stopping times than in the original Azema-Yor algorithm. The Skorokhod embedding problem has generated recent interest, motivated by connections to optimal stopping problems. The optimal stopping problem in mathematical nance is concerned with choosing a time (or a family of times) to exercise an exotic option, such that the reward is maximized (or the cost is minimized). We shall illustrate the optimal stopping problems in mathematical nance via existing Skorokhod embedding algorithms. This talk is based on joint work with Marc Yor.
Contact Information:
Name: Pavel Grinfeld
Email: pg77@drexel.edu
Korman Center, Room 245, 15 S. 33rd Street, Philadelphia, PA 19104
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