We provide an axiomatic definition of conditional submodular capacity that allows conditioning on “null” events and is the basis for the notions of consistency and of consistent extension of a partial assessment. The same definition gives rise to an axiomatic definition of conditional submodular Choquet expected value, which is a conditional functional defined on conditional gambles, that can be expressed as the Choquet integral with respect to its restriction on conditional indicators. Finally, the notion of conditional submodular Choquet expected value is used to provide a definition of conditional submodular coherent risk measure that, locally on every conditioning event, has an upper expected loss interpretation.

Conditional submodular Choquet expected values and conditional coherent risk measures / Petturiti, D.; Vantaggi, B.. - In: INTERNATIONAL JOURNAL OF APPROXIMATE REASONING. - ISSN 0888-613X. - 113:(2019), pp. 14-38. [10.1016/j.ijar.2019.06.004]

Conditional submodular Choquet expected values and conditional coherent risk measures

Vantaggi B.
2019

Abstract

We provide an axiomatic definition of conditional submodular capacity that allows conditioning on “null” events and is the basis for the notions of consistency and of consistent extension of a partial assessment. The same definition gives rise to an axiomatic definition of conditional submodular Choquet expected value, which is a conditional functional defined on conditional gambles, that can be expressed as the Choquet integral with respect to its restriction on conditional indicators. Finally, the notion of conditional submodular Choquet expected value is used to provide a definition of conditional submodular coherent risk measure that, locally on every conditioning event, has an upper expected loss interpretation.
2019
Conditional Choquet expected value; Conditional coherent risk measure; Conditional submodular capacity
01 Pubblicazione su rivista::01a Articolo in rivista
Conditional submodular Choquet expected values and conditional coherent risk measures / Petturiti, D.; Vantaggi, B.. - In: INTERNATIONAL JOURNAL OF APPROXIMATE REASONING. - ISSN 0888-613X. - 113:(2019), pp. 14-38. [10.1016/j.ijar.2019.06.004]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1355395
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