Fuzzy measures and asset prices: accounting for information ambiguity
Author:
Umberto Cherubini a
| Affiliation: | a Banca Commerciale Italiana, Economic Research Department, Via Borgonuovo, 2, 20121 Milan, Italy. |
DOI:
10.1080/135048697334773
Publication Frequency:
6 issues per year
Number of References: 34
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Abstract
A recent stream of literature has suggested that many market imperfections or 'puzzles' can be easily explained once information ambiguity, or knightian uncertainty is taken into account. Here we propose a parametric representation of this concept by means of a special class of fuzzy measures, known as gλ-measures. The parameter λ may be considered an indicator of uncertainty. Starting with a distribution, a value λ in (0, ∞) and a benchmark utility function we obtain a sub-additive expected utility, representing uncertainty aversion. A dual value λ* in (-1, 0) defining a super-additive expected utility is also recovered, while the benchmark expected utility is obtained for λ = λ* = 0. The two measures may be considered as lower and upper bounds of expected utility with respect to a set of probability measures, in the spirit of Gilboa-Schmeidler MMEU theory and of Dempster probability interval approach. The parametrization may be used to determine the effect of information ambiguity on asset prices in a very straightforward way. As examples, we determine the price of a corporate debt contract and a 'fuzzified' version of the Black and Scholes model.
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| Keywords: Knightian Uncertainty; Market Incompleteness; Non-additive Measures; Asset Pricing |
| view references (34) : view citations |

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