Description

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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.

Organizers

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T B
Tomasz Bielecki Applied Mathematics, Illinois Institute of Technology
R C
Rama Cont Mathematics Institute, Oxford University
X G
Xin Guo IEOR, University of California, Berkeley
L H
Lars Hansen Economics, University of Chicago
P K
Peter Klibanoff Managerial Economics & Decision Sciences, Kellogg School of Management, Northwestern University
M N
Marcel Nutz Statistics, Columbia University
T Z
Thaleia Zariphopoulou Mathematics and IROM, McCombs School of Business, University of Texas at Austin

Program Workshops

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Workshop
Advances in Optimal Decision Making under Uncertainty
expanded

This workshop will bring together experts and young researchers interested in the most recent developments of mathematical finance and insurance in both academia and industry. Experts will present state of the art topics in among others, fintech, high-frequency trading, robo-advising, risk measures, market impact and optimal execution, reinsurance, and commodity and energy markets. Talks on recent theoretical advances in BSDE systems, robust optimization in pricing and hedging, relaxed control in reinforcement learning, and decision-making under non-standard criteria will be also presented.

Workshop
Confronting Uncertainty in Climate Change
expanded

Climate change is well-recognized as an important economic, social, and political challenge. To develop meaningful quantitative models that guide prudent policymaking requires methods that quantify the pertinent uncertainty and approaches to incorporate them into the assessment of alternative courses of action. This workshop will bring together decision theorists, geoscientists and economists to discuss recent advances in stochastic modeling, uncertainty quantification and applications to the economics of climate change.

Workshop
Decision Making under Uncertainty
expanded

Decision Theory, including its applications and closely-related topics, is a deep and active area of research. It includes theories of how people make or should make decisions, often in the face of uncertainty. Mathematically, such theories often connect preferences or choices with functional representations, and/or analyze and apply such functionals as models of behavior. At this workshop, invited scholars will present their recent work and engage in discussion with the audience.

Workshop
Dynamic Assessment Indices
expanded

Over the past two decades significant progress has been made in developing a general framework for studying preference orders in an uncertain and dynamic environment, primarily with applications to risk management, economics, pricing and hedging, as well as stochastic optimal control. The theory and practice of assessment indices is an integral part of this general framework. At abstract level, an assessment index is a functional defined on the set of objects to be ordered that satisfies a set of minimal assumptions, such as monotonicity (better for better) and quasi-concavity (diversification is preferred to concentration). In particular, assessment indices can be used in rendering a trade-off between reward opportunities and risk of losses. Some of the key research directions in this area are: (a) finding analytically tractable descriptions of such classes of functionals; (b) establishing adequate description of intertemporal properties, also known as time (in)consistency in decision making.

Workshop
Applied Optimal Transport
expanded

This workshop showcases current developments in theoretical and computational optimal transport with a focus on applications in machine learning and statistics.

Application

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