Conditional submodular Choquet expected values and conditional coherent risk measures
| Autor: | Davide Petturiti, Barbara Vantaggi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Applied Mathematics
Conditional coherent risk measure 02 engineering and technology Expected value Theoretical Computer Science Submodular set function Conditional submodular capacity Conditional Choquet expected value Conditional submodular capacity Conditional coherent risk measure Null (SQL) Choquet integral Artificial Intelligence Conditional Choquet expected value 020204 information systems Coherent risk measure 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Expected loss Mathematical economics Software Axiom Event (probability theory) Mathematics |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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