Certainty Equivalent: Many Meanings of a Mean

Pagani, Elisa

doi:10.2139/ssrn.2615728

Cited by 2 publications

(2 citation statements)

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“…In the literature, there are different certainty equivalent concepts for d > 1 when a complete preference relation admitting a single-prior single-utility representation with a multivariate utility function is considered, see the survey [30]. In [30], it is stated that no vector-valued or set-valued certainty equivalent concept has been introduced for multivariate utility functions so far. However, a set-valued certainty equivalent definition is provided in [34] for a multi-asset game setting.…”

Section: Introductionmentioning

confidence: 99%

Certainty equivalent and utility indifference pricing for incomplete preferences via convex vector optimization

Rudloff

Ulus

2020

Math Finan Econ

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For incomplete preference relations that are represented by multiple priors and/or multiplepossibly multivariate-utility functions, we define a certainty equivalent as well as the utility indifference price bounds as set-valued functions of the claim. Furthermore, we motivate and introduce the notion of a weak and a strong certainty equivalent. We will show that our definitions contain as special cases some definitions found in the literature so far on complete or special incomplete preferences. We prove monotonicity and convexity properties of utility buy and sell prices that hold in total analogy to the properties of the scalar indifference prices for complete preferences. We show how the (weak and strong) set-valued certainty equivalent as well as the indifference price bounds can be computed or approximated by solving convex vector optimization problems. Numerical examples and their economic interpretations are given for the univariate as well as for the multivariate case.

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Section: Introductionmentioning

confidence: 99%

Certainty equivalent and utility indifference pricing for incomplete preferences via convex vector optimization

Rudloff

Ulus

2020

Math Finan Econ

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“…The notion seems to have appeared in connection with the concept of certain equivalent. Some review papers, emphasizing the connection of generalized means to utility theory are Muliere and Parmigiano's [17] and Pagani's [16]. 1 Consider Matkowski and Páles [14] or Páles [18], in which a large number of the original papers are reviewed.…”

Section: Introductionmentioning

confidence: 99%

A predictive approach to generalized arithmetic means

Gzyl

2020

Preprint

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The goal of this note is to provide a geometric setting in which generalized arithmetic means are best predictors in an appropriate metric. This characterization provides a geometric interpretation to the concept of certainty equivalent. Besides that, in this geometric setting there also exists the notion of conditional expectation as best predictor given prior information. This leads to a notion of conditional preference and to the notion of conditional certainty equivalent, which turns out to be consistent with the notion of fair pricing.

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Certainty Equivalent: Many Meanings of a Mean

Cited by 2 publications

References 73 publications

Certainty equivalent and utility indifference pricing for incomplete preferences via convex vector optimization

Certainty equivalent and utility indifference pricing for incomplete preferences via convex vector optimization

A predictive approach to generalized arithmetic means

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