A New Integral for Capacities
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 e...
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| Veröffentlicht in: | Economic theory 2009-04, Vol.39 (1), p.157-176 |
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| creator | Lehrer, Ehud |
| description | 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. |
| doi_str_mv | 10.1007/s00199-007-0302-z |
| format | Article |
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The extension to fuzzy capacities enables one to calculate the integral also in cases where the information available is limited to a few events.</description><subject>Betting</subject><subject>Decision making</subject><subject>Decision theory</subject><subject>Economic theory</subject><subject>Economic Theory/Quantitative Economics/Mathematical Methods</subject><subject>Economics</subject><subject>Economics and Finance</subject><subject>Expected utility</subject><subject>Expected values</subject><subject>Game Theory</subject><subject>Mathematical functions</subject><subject>Mathematical integrals</subject><subject>Mathematical minima</subject><subject>Microeconomics</subject><subject>Probability</subject><subject>Probability distribution</subject><subject>Probability distributions</subject><subject>Public Finance</subject><subject>Random variables</subject><subject>Research Article</subject><subject>Risk aversion</subject><subject>Social and Behav. 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| ispartof | Economic theory, 2009-04, Vol.39 (1), p.157-176 |
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| source | SpringerNature Journals; EBSCOhost Business Source Complete; JSTOR Archive Collection A-Z Listing |
| subjects | Betting Decision making Decision theory Economic theory Economic Theory/Quantitative Economics/Mathematical Methods Economics Economics and Finance Expected utility Expected values Game Theory Mathematical functions Mathematical integrals Mathematical minima Microeconomics Probability Probability distribution Probability distributions Public Finance Random variables Research Article Risk aversion Social and Behav. Sciences Studies Uncertainty |
| title | A New Integral for Capacities |
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