Informacja o goĊciu:
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.
Streszczenie:
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.