On decision making in probability models with uncertainty

A. Shiryaev
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A. Shiryaev: Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Journal of the New Economic Association, 2024, vol. 65, issue 4, 12-29

Abstract: In the modern theory of probability the basic notion is "probabilistic space" on which the notions of random variables and their expectations are defi ned. These elements give, in particular, a possibility to determine the quality of decisions, to defi ne decision functions and their quality. At the same time in probability models with uncertainty we need to consider instead of one probability space a family of such spaces. For this case of uncertainty we have notions of sublinear and nonlinear expectations, g-expectations, backward stochastic differential equations, notions of Choquet capacity and integrals. The classical law of large number has a new form under assumption of uncertainty. The present paper has an overview character and is aimed to attract the readers' attention to new probabilistic aspects of modeling under uncertainty and to corresponding tools of investigation. The paper is an extended version of the author's report at the seminar on mathematical economics of V. I. Danilov and V. M. Polterovich at Moscow School of Economics, MSU, given on 30 January 2024.

Keywords: probabilistic-uncertain models; utility functions; Allais and Ellsberg paradoxes; capacity and Choquet integral; inverse stochastic differential equations; upper and lower prices (search for similar items in EconPapers)
JEL-codes: C6 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:nea:journl:y:2024:i:65:p:12-29

DOI: 10.31737/22212264_2024_4_12-29

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