**Decision Making and Uncertainty**

### Spring 2022 Long Program

### March 21-May 27, 2022

**Organizers**:

- Lars Hansen (Economics, University of Chicago)
- Tomasz Bielecki (Applied Mathematics, Illinois Institute of Technology)
- Rama Cont (Mathematics Institute, Oxford University)
- Xin Guo (IEOR, University of California, Berkeley)
- Peter Klibanoff (Managerial Economics & Decision Sciences, Kellogg School of Management, Northwestern University)
- Marcel Nutz (Statistics, Columbia University)
- Thaleia Zariphopoulou (Mathematics and IROM, McCombs School of Business, University of Texas at Austin)

Economics, finance, and business activities like marketing, operations management, and R&D all substantially rely on the use of formal, mathematical approaches to model human behavior, agents’ interaction, trading exchanges, mitigation of risks, and more. However, these areas are all rich enough that many important challenges are as yet unmet and new ones are constantly arising. For example, recent advances in data science, new platforms and means of human interaction, the growing speed of trading exchanges and flow of information, and various technological and other breakthroughs are all fertile ground motivating the use of new mathematical and statistical models and methods.

The mathematical sciences can play a crucial role by providing a platform on which to build and analyze innovative and complex models and as well as rigorous frameworks to solve the associated problems. However, this alone is not enough to make breakthrough progress. An intense scientific dialogue is needed so that the analysis of real-world problems may benefit from mathematical and statistical innovations, while, at the same time, the discipline and focus provided by such problems may help the mathematics from becoming remote from the real-world challenges. The intention of this program is to create and facilitate such an interdisciplinary dialogue by bringing together mathematicians, statisticians, economists, computer scientists, and researchers from operations research and business.

While there are many areas in need of high-level mathematical and statistical analysis, the program will focus on two broad directions covering a quite large spectrum of problems in social sciences.

The first direction is decision making and optimization (e.g. of expected utility or expected costs) under model ambiguity and potential misspecification. Partial or incomplete model knowledge are present in the analysis of any real-world application. Moreover, quantitative models used in decision making are necessarily simplified abstractions and necessarily “wrong.’’ This misspecification could be innocuous. or it could have big consequences for decision makers. For example, pension fund management requires good models and forecasts about economic growth which is notoriously difficult to do with much precision over long horizons. Prudent policies designed to confront climate change must confront both geo scientific and economic uncertainty. High frequency trading needs assessment of the upcoming, even to the millisecond, asset price fluctuations. Real-world applications involve decisions at both the personal (single-agent) and collective (multi-agent, games, etc.) level. Frequently, model ambiguity from multiple sources can have percolating impact that compounds over time. For example, in so-called integrated assessment models, geo scientific uncertainty about consequences of carbon emissions and the uncertainty about the potential economic and social damages can be reinforcing and have serious consequences on macroeconomic decisions and policies. In general, optimizing under misconceived simplifications may result in large losses, severe mismanagement and flawed valuation, etc. Thus the manner in which uncertainty is navigated not affect individuals like investors, fund managers, and pensioners, but also communities, municipalities, states, and society on the aggregate.

The second direction is the interface between decision making and machine learning*.* The recent explosive progress in machine learning provides a wide array of powerful optimization tools. On the other hand, a plethora of more complex problems related to the learning and modeling of human preferences and behavior and, in turn, their role and impact in decision making are now emerging quickly. These problems require much more sophisticated analysis, well beyond the ones in most existing ML settings with stylized cost/payoff functionals (square error, convex losses, concave utilities, etc.). They arise in many real-world applications related to decisions of investors, patients, consumers, pensioners, voters, etc., at both personal and collective levels. Furthermore, many such applications are now incorporating human-machine interaction (e.g. robo-advising), and this requires the development of additional modeling, methodological, and technical approaches and tools. In parallel, recent methodological advances in data analysis based on optimal transport provide new ways of studying ML problems, and give rise at the same time to new mathematical models and new problems at the interfaces between data analysis, machine learning, optimization, and decision making.

The activities of the program will include presentations by the participants (long- and short-term visitors), panel discussions, talks by industry researchers and others, and a number of week-long thematic workshops that will focus on specific applications, paired with presentations on modeling aspects as well as on related methodologies and technical approaches. It will also include workshops primarily focused on recent mathematical advances aiming at presenting new technical knowledge that can be used to build better models and define new mathematical problems related to applications. An introduction to the program, both in terms of topics and activities, is the summer month long tutorial Introduction to Decision Making and Uncertainty scheduled to take place at IMSI during July 2021.

Workshops which will take place as part of this program include:

**Applied Optimal Transport**organized by Marcel Nutz**Machine learning with applications to finance**organized by Xin Guo**Systemic risk and stress testing**organized by Rama Cont**Dynamic Assessment Indices**organized by Tomasz Bielecki**Optimization in human-machine interaction systems**organized by Thaleia Zariphopoulou**Decision making under Uncertainty**organized by Peter Klibanoff**Climate change uncertainty spillovers for policy and markets**organized by Lars Hansen