CCMS Colloquium: Distribution-Based Optimal Asset Selling — Sixian Jin (CSU San Marcos)

Abstract: In this talk, we study the optimal timing of selling a risky asset within the distribution builder framework. Instead of specifying a utility function or risk-aversion parameter, this approach allows an investor to express preferences directly through a desired distribution of the selling price. Mathematically, the problem is closely related to the Skorokhod embedding problem, where a target distribution is attained by stopping a diffusion process. We first discuss the distribution builder problem for general one-dimensional diffusions and then extend the framework to incorporate the possibility of ruin, which places additional restrictions on the distributions that can be attained. We characterize the set of distributions attainable before ruin and consider two related optimization problems: finding the attainable distribution closest to an unattainable target, and improving an attainable target under first-order stochastic dominance constraints. Using an extended f-divergence framework, we establish existence and uniqueness results, provide analytic characterizations of the solutions, and illustrate the approach with numerical examples.

Sixian Jin is an Assistant Professor of Mathematics at California State University San Marcos. He graduated from Claremont Graduate University in 2017 under the supervision of Prof. Henry Schellhorn. His research interests include stochastic analysis, stochastic differential equations, and their applications in mathematical finance. In addition to his research, he is actively involved in undergraduate and graduate education in probability, statistics, and financial mathematics. He is also interested in the use of artificial intelligence in mathematics education, particularly in exploring how AI tools can be effectively incorporated into the teaching and learning of financial mathematics and statistics.

For questions about the event, please contact your CCMS Colloquium chairs:

Prof. Robert Cass (Robert.Cass@ClaremontMcKenna.edu) or Prof. Qidi Peng (Qidi.Peng@cgu.edu)

For logistical questions, contact Maxwell Kooiker (Maxwell.Kooiker@cgu.edu), the CCMS Colloquium Assistant.