# 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

, Volume 4 (3): 15 – Sep 1, 1997
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...

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Publisher
Taylor & Francis
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 FinanceTaylor & Francis

Published: Sep 1, 1997

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