A new integral for capacities View Full Text


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Article Info

DATE

2007-10-30

AUTHORS

Ehud Lehrer

ABSTRACT

A new integral for capacities is introduced and characterized. It differs from the Choquet integral on non-convex capacities. The main feature of the new integral is concavity, which might be interpreted as uncertainty aversion. The integral is extended to fuzzy capacities, which assign subjective expected values to random variables (e.g., portfolios) and may assign subjective probability only to a partial set of events. An equivalence between the minimum over sets of additive capacities (not necessarily probability distributions) and the integral w.r.t. fuzzy capacities is demonstrated. The extension to fuzzy capacities enables one to calculate the integral also in cases where the information available is limited to a few events. More... »

PAGES

157-176

References to SciGraph publications

  • 1998-08. Axiomatic characterizations of the Choquet integral in ECONOMIC THEORY
  • 2001. On law invariant coherent risk measures in ADVANCES IN MATHEMATICAL ECONOMICS
  • 1983. Submodular functions and convexity in MATHEMATICAL PROGRAMMING THE STATE OF THE ART
  • 2006-04-05. Market Games in Large Economies with a Finite Number of Types in ECONOMIC THEORY
  • 1982-09. Cooperative games with large cores in INTERNATIONAL JOURNAL OF GAME THEORY
  • 1992-10. Recent developments in modeling preferences: Uncertainty and ambiguity in JOURNAL OF RISK AND UNCERTAINTY
  • 2002. Coherent Risk Measures on General Probability Spaces in ADVANCES IN FINANCE AND STOCHASTICS
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    http://scigraph.springernature.com/pub.10.1007/s00199-007-0302-z

    DOI

    http://dx.doi.org/10.1007/s00199-007-0302-z

    DIMENSIONS

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