Publications in Scientific Journals:
M. Beiglböck, M. Eder, C. Elgert, U. Schmock:
"Geometry of Distribution-Constrained Optimal Stopping Problems";
Probability Theory and Related Fields,
We adapt ideas and concepts developed in optimal transport (and
its martingale variant) to give a geometric description of optimal stopping times τ of Brownian motion subject to the constraint that the distribution of τ is a given probability µ. The methods work for a large class of cost processes. (At a minimum we need the cost process to be measurable and (F0 t)t≥0-adapted. Continuity assumptions can be used to guarantee existence of solutions.)
We find that for many of the cost processes one can come up
with, the solution is given by the first hitting time of a barrier in a suitable phase space. As a by-product we recover classical solutions of the inverse first passage time problem / Shiryaev´s problem.
distribution-constrained optimal stopping, optimal transport, inverse first passage problem, Shiryaev´s problem MSC (2010) Primary 60G42, 60G44; Secondary 91G20
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.