Instytut Matematyki Stosowanej i Mechaniki Wydziału Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego oraz Oddział Warszawski Polskiego Towarzystwa Matematycznego

W dniu 27-02-2020 roku (CZWARTEK) o godz. 12:15 w sali 2180 Wydziału Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego, ul. Banacha 2 w Warszawie w ramach Konwersatorium Instytutu Matematyki Stosowanej i Mechaniki UW oraz Oddziału Warszawskiego PTM

Profesor Andrzej P. Ruszczyński (Rutgers University, USA)

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RISK FORMS: DUALITY, DISINTERGRATION AND STATISTICAL ESTIMATION

Abstract:
We introduce the concept of a risk form, which is a real functional on the product of two spaces: the space of measurable functions and the space of measures on a Polish space. We present a dual representation of risk forms and generalize the classical Kusuoka representation to this setting. For a risk form acting on a product space, we define marginal and conditional forms and we prove a disintegration formula, which represents a risk form as a composition of its marginal and conditional forms. We apply the proposed approach to two-stage optimization problems with partial information and decision-dependent observation distribution. Finally, we discuss statistical estimation of risk forms and present a central limit formula for a class of forms defined by nested expectations.

About speaker:
Andrzej P. Ruszczyński received his PhD and habilitation degrees in control engineering from Warsaw University of Technology in 1976 and 1983, respectively. He has been with Warsaw University of Technology (Poland), University of Zurich (Switzerland), International Institute of Applied Systems Analysis (Laxenburg, Austria), Princeton University, University of Wisconsin-Madison, and Rutgers University. Dr. Ruszczyński is one of the creators of and main contributors to the field of risk-averse optimization, author of "Nonlinear Optimization" (Princeton University Press, 2006), co-author of "Lectures on Stochastic Programming" (SIAM, 2009), "Stochastic Programming" (Elsevier, 2003), and author of more than 100 articles in the area of optimization. He is the recipient of the 2018 Dantzig Prize of SIAM and the Mathematical Optimization Society, and an INFORMS fellow.

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https://en.wikipedia.org/wiki/Andrzej_Piotr_Ruszczy%C5%84ski