Risk Forms: Duality, Disintegration, and Statistical Estimation

Prelegent(ci)

Andrzej Ruszczyński

Afiliacja

Rutgers University

Język referatu

angielski

Termin

27 lutego 2020 14:15

Pokój

p. 2180 (sala RW)

Tytuł w języku polskim

Risk Forms: Duality, Disintegration, and Statistical Estimation

Seminarium

Konwersatorium IMSM

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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 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.

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