How do we make decisions in the face of risk? The need to make decisions in the presence of uncertainty cuts across a wide range of issues in science and human behavior. The underlying problems require both sophisticated modeling and advanced mathematical and statistical approaches and techniques.

This program will serve as an introduction to the long program on Decision Making and Uncertainty scheduled for Spring 2022. It aims to introduce participants to a variety of modeling questions and methods of current interest in this area. It will be built on “thematic clusters” of emerging areas of application.

Each cluster will begin with tutorial lectures on the first day followed by supporting lectures on mathematical and statistical topics related to the underlying theme. There will also be panel discussions, together with poster sessions and short presentations by the participants.

The intended audience is researchers interested in mathematical modeling and methods applicable to decision making under uncertainty in economics, finance, business, and other areas. Advanced Ph.D. students, postdocs, and junior faculty are especially encouraged to apply.

The program covers a diverse set of topics and each theme will be self-contained. Given the variety of both the applications and the methods, participants are encouraged to attend the entire program. Basic knowledge in probability, stochastics, and statistics is required.

The planned clusters are as follows.

June 28-July 2Foundations of stochastic optimization, Dynamic Programming, and Hamilton-Jacobi-Bellman equationsThaleia Zariphopoulou (Mathematics and McCombs Business School, University of Texas at Austin)
July 5-7Optimal transport and machine learningMarcel Nutz (Statistics, Columbia University)
July 8-9Time-inconsistent and relaxed stochastic optimization, and applicationsXunyu Zhou (IEOR, Columbia University)
July 12-16Markov decision processes with dynamic risk measures: optimal control and learningTomasz Bielecki (IIT) and Andrzej Ruszczynski (Rutgers Business School)
Machine learning and Mean Field GamesXin Guo (IEOR, Berkeley)
July 19-23Models for climate change with ambiguity and misspecification concernsLars Hansen (Economics, University of Chicago)
Games with ambiguityPeter Klibanoff (Kellogg School, Northwestern University)

Week 1: June 28-July 2

Module: Foundations of stochastic optimization, BSDE and applications

Organizer: Thaleia Zariphopoulou (McCombs Business School and Mathematics, UT Austin) 

Module Summary

Monday, June 28

8:45-9:00 Welcome and introduction to the spring long program, Takis Souganidis (University of Chicago)

Title: Foundations of stochastic optimization

Speaker: Thaleia Zariphopoulou (UT-Austin) 

Description & Schedule

Tuesday, June 29

Title:  Probabilistic methods for elliptic and parabolic PDEs: from linear equations to free-boundary problems

Speaker: Sergey Nadtochiy (IIT) 

Description & Schedule

Wednesday, June 30

Title: Foundations of Backward Stochastic Differential Equations and their applications

Speakers:   Gordan Zitkovic (UT-Austin) and Joseph Jackson (UT-Austin)  

Description & Schedule

Thursday, July 1

Title: Introduction to Functional Itô Calculus and applications

Speaker: Rama Cont  (Oxford University) 

9:00-10:15: Lecture 1
10:45-12:00: Lecture 2

Friday, July 2

Title: Introduction to robo-advising: modeling, learning, and human-machine interactions

Speakers:  Agostino Capponi (Columbia University) and Sveinn Olafsson (Columbia University)

Description & Schedule

Week 2:  July 5-9

Monday, July 5  Holiday

July 6-7  

Module: Optimal transport and machine learning 

Organizer: Marcel Nutz (Mathematics and Statistics, Columbia University)

Module Summary

Tuesday, July 6

9:00 Introduction to optimal transport
Marcel Nutz (Columbia University)


1:00 Distribution-free nonparametric inference using optimal transport
Bodhisattva Sen (Columbia University)


July 7

9:00 Learning with optimal transport
Aude Genevay (MIT)


1:00 Statistical estimation and optimal transport
Jonathan Niles-Weed (NYU)


July 8-9 

Module: Time-inconsistent  and relaxed stochastic optimization, and  applications

Organizer: Xunyu Zhou (Columbia University)

Module Summary

Thursday, July 8

Speakers:  Xunyu Zhou (Columbia University) and Wenpin Tang (Columbia University) 

Title: Exploration via Randomization: Reinforcement Learning and Beyond

Description and Schedule

Friday, July 9

Speakers:  Xuedong He (CUHK) and Moris Strub (SUSTECH)  

Title: Foundations of time-inconsistent control, and applications to decision making under non-standard optimality criteria

Description and Schedule

Week 3: July 12-16

Module 1: Markov decision processes with dynamic risk measures: optimal control and learning 

Organizers: Tomasz Bielecki (IIT) and Andrzej Ruszczyński (Department of Management Science and Information Systems, Rutgers)

Module 2: Machine learning and Mean Field Games 

Organizer: Xin Guo (IEOR, UC Berkeley)

Monday, July 12

Schedule & Descriptions

Tuesday, July 13

Schedule and Descriptions

Wednesday, July 14

Schedule & Description

Thursday, July 15

Schedule & Description

Friday, July 16

Workshop Schedule (Module 1)

Week 4: July 19-22

Module 1:  Models for climate change with ambiguity and misspecification concerns 

Organizer: Lars Hansen (Economics, University of Chicago)

Module 2:  Games with ambiguity 

Organizer: Peter Klibanoff (Managerial Economics & Decision Sciences, Kellogg School of Management, Northwestern University)

Module Summary

Monday, July 19


Tuesday, July 20


Wednesday, July 21


Thursday, July 22