Home > Events > 2018 Seminars & Colloquia > Andrzej Ruszczynski, Rutgers University

Andrzej Ruszczynski, Rutgers University

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Risk Forms: Duality, Disintegration, and Statistical Estimation
When
20 September 2018 from 4:00 PM to 5:00 PM
Where
201 Thomas Building
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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 forRisk Forms: Duality, Disintegration, and Statistical Estimation

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.mula, 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.

Andrzej Ruszczynski 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. Ruszczynski 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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