Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Fuzzy measures and asset prices: accounting for information ambiguity

Fuzzy measures and asset prices: accounting for information ambiguity 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 g λ-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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematical Finance Taylor & Francis

Fuzzy measures and asset prices: accounting for information ambiguity

Cherubini, Umberto
Applied Mathematical Finance , Volume 4 (3): 15 – Sep 1, 1997
Download PDF
15 pages

Fuzzy measures and asset prices: accounting for information ambiguity

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 g λ-measures. The parameter λ may be considered an indicator of uncertainty. Starting with a distribution, a value λ in (0, ∞) and a benchmark utility...
Loading next page...
 
/lp/taylor-francis/fuzzy-measures-and-asset-prices-accounting-for-information-ambiguity-yBI7SaWsDL
Publisher
Taylor & Francis
Copyright
Copyright Taylor & Francis Group, LLC
ISSN
1466-4313
eISSN
1350-486X
DOI
10.1080/135048697334773
Publisher site
See Article on Publisher Site

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 g λ-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.

Journal

Applied Mathematical Finance – Taylor & Francis

Published: Sep 1, 1997

Keywords: Knightian Uncertainty; Market Incompleteness; Non-additive Measures; Asset Pricing

There are no references for this article.