Risk Forms: Duality, Disintegration, and Statistical Estimation

Speaker(s)

Andrzej Ruszczyński

Affiliation

Rutgers University

Language of the talk

English

Date

Feb. 27, 2020, 2:15 p.m.

Room

room 2180 (sala RW)

Title in Polish

Risk Forms: Duality, Disintegration, and Statistical Estimation

Seminar

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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