A new integral for capacities

被引：0
作者：
Ehud Lehrer
机构：
[1] Tel Aviv University,School of Mathematical Sciences
[2] INSEAD,undefined
来源：
Economic Theory | 2009年 / 39卷
关键词：
Capacities; Non-additive probability; Decisions under uncertainty; Uncertainty aversion; Concave integral; Choquet integral; Fuzzy capacities; Large core; C71; D80; D81; D84;
D O I：
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学科分类号：
摘要：
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.
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页码：157 / 176
页数：19
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共 38 条
  • [1] Artzner P.(1998)Coherent measures of risk Financ Stoch 9 203-228
  • [2] Delbaen F.(2007)Market games in large economies with a finite number of types Econ Theory 31 327-342
  • [3] Eber J.-M.(2007)Extendable cooperative games J Public Econ Theory 9 1069-1078
  • [4] Heath D.(1962)The theory of the core in an Vestn Leningr Univ 13 141-142
  • [5] Azrieli Y.(1992)-person game (in Russian) J Risk Uncertain 5 325-370
  • [6] Lehrer E.(1992)Recent developments in modelling preferences: uncertainty and ambiguity Econometrica 60 197-204
  • [7] Azrieli Y.(1994)Uncertainty aversion, risk aversion, and the optimal choice of portfolio J Econ Theory 64 305-324
  • [8] Lehrer E.(1987)Nash equilibrium under Knightian uncertainty J Math Econ 16 65-88
  • [9] Bondareva O.(1989)Expected utility with purely subjective non-additive probabilities J Math Econ 18 141-153
  • [10] Camerer C.F.(1998)Maxmin expected utility with non-unique prior Econ Theory 12 441-448
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