Grant: Discovery Grants Program - Individual

Decisions often need to be made in situations where one has incomplete knowledge about some of the parameters of the problem that they are addressing. This is for example the case in a problem of portfolio selection where the future value of an asset is uncertain, or in an inventory management problem where the future market demand for a product might change. While there are situations in which the uncertainty and the desired risk attitude can be fully characterized using a distribution model and a risk measure, in most situations it is impossible to identify these precisely and unequivocally. One might for instance recall the debates surrounding the Basel II and III accord around how to quantify risk (i.e. regarding the use of variance, value at risk, or expected shortfall). One might also think about the multiplicity of opinions regarding the rate at which climate changes might affect agriculture, health, and wildlife. Finally, the recent pandemic also demonstrated to us that the most critical decisions (i.e. whether to close or not borders, confine the population, and what sanitary measures to put in place) often arise in situations where very little is known about the likelihood of the different outcomes. Fortunately, in the era of "Big data", it is also starting to become common practice for decision maker to extract information from immense historical datasets while taking precautions regarding statistical significance of the conclusions, and the possibility that the past might not give us accurate information about the future. This research program has the objective of shedding some light on how to properly and efficiently handle the uncertainty that plagues decision problems emerging from a wide range of applications, with a special attention to methods that can make best use of available data. It has three major dimensions which are summarized by the following questions: �How should decisions be made when the exact nature of the factors influencing the performance of the decision are unknown, and in particular when a large volume of historical data is available? �How can one find optimal decisions that truly reflects the compromises that a decision maker (or group of decision makers) is willing to make between risk and returns, or between conflicting objectives, while protecting him against inherent cognitive biases? �How can optimal decisions be generated efficiently when problems take on realistic sizes? To make progress with respect to these questions, the program will investigate important open problems in the following fields: robust optimization, distributionally robust optimization, contextual optimization, and preference robust optimization. Finally, the theoretical and numerical progresses that are expected above will continuously be evaluated and motivated with applications in finance, inventory management, logistics, disaster preparedness, and emergency medical services.