We revisit the question of the optimal time of an asset sale from the point of view of Sharpe's "Distribution Builder" approach: Instead of assuming the investor's risk preferences in form of a utility function, the investor provides themself a distribution that should be attained when selling the asset at a stopping time (specified a priori). This obviously begs the questions which distributions are attainable for an investor. We connect this problem to the Skorokhod embedding problem for one-dimensional diffusions and provide explicit representation for optimal stopping times as well as their expected values. In the case that the target distribution is specified from a parametrized family (e.g., log-normal distributions), we show that optimality involves a mean-variance trade-off similar to the efficient frontier in Markowitz's approach to portfolio optimization. This is joint work with Peter Carr.

Speaker Bio: Stephan Sturm is Associate Professor of Mathematical Sciences at Worcester Polytechnic Institute (WPI) in Massachusetts and currently spends his sabbatical at the Chinese University of Hong Kong and NYU. After obtaining his PhD in Mathematics from TU Berlin (Germany), he became a Postdoctoral Research Associate and Lecturer at the Department of Operations Research and Financial Engineering at Princeton University before joining WPI as faculty member. Sturm's research covers mainly different areas of financial mathematics, but he is interested in stochastic modeling in general, such as applications to climate science. In finance, his work is devoted in particular in questions of value adjustments for derivative securities (XVAs), optimal portfolio selection and systemic risk in financial markets.