Prof. Dr. Stefan Ankirchner : The Skorokhod embedding problem for homogeneous diffusions and applications to stopping contests
Prof. Dr. Stefan Ankirchner (University of Bonn) holder et seminar med tittelen: The Skorokhod embedding problem for homogeneous diffusions and applications to stopping contests
We consider the Skorokhod embedding problem (SEP) for a general time-homogeneous diffusion $X$: given a distribution $\rho$, is there a stopping time $\tau$ such that the stopped process $X$ has the distribution $\rho$? We present a solution method that makes use of martingale representations and draws on law uniqueness of weak solutions of SDEs. Then we ask if there exist solutions of the SEP which are respectively finite almost surely, integrable or bounded, and when does our proposed construction have these properties. We provide conditions that guarantee existence of finite time solutions. Moreover, we fully characterize the distributions that can be embedded with integrable stopping times, and we derive necessary, respectively sufficient, conditions under which there exists a bounded embedding. Finally we apply the results to winner-take-all contests where agents aim at stopping a process at a highest possible value.
The talk is based on joint work with David Hobson and Philipp Strack.