Decreasing Ross risk aversion : higher-order generalizations and implications

Jianli WANG, Jingyuan LI

Research output: Journal PublicationsJournal Article (refereed)Researchpeer-review

Abstract

We define decreasing higher-degree Ross risk aversion and provide an intuitive interpretation for it. We show that all deteriorations of background risk in the sense of n -th risk increase raise risk aversion in the Arrow-Pratt sense if and only if decreasing ( n + 1 ) -th degree Ross risk aversion holds. Meanwhile, the utility functional form of the agent with decreasing ( n + 1 ) -th degree Ross risk aversion is specified. Our result also implies decreasing 3-rd degree Ross risk aversion can be used to characterize the sufficient condition of risk vulnerability. Moreover, our analysis shows the implication of decreasing n / m -th ( n > m ≥ 1 ) Ross risk aversion.
Original languageEnglish
Pages (from-to)136-142
Number of pages7
JournalJournal of Mathematical Economics
Volume55
Early online date26 Feb 2014
DOIs
Publication statusPublished - Dec 2014

Fingerprint

Risk Aversion
Higher Order
Deterioration
Vulnerability
Generalization
Risk aversion
Intuitive
If and only if
Imply
Sufficient Conditions

Bibliographical note

This research was supported by the Faculty Research Grant of Lingnan University under Research Project No. DR12A9, Direct Grant for Research of Lingnan University under Research Project No. DR13C8 and the Fundamental Research Funds for the Central Universities under Research Project No. NR2014002.

Keywords

  • Background risk
  • Decreasing n-th Ross risk aversion
  • Risk vulnerability: one-switch utility function

Cite this

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title = "Decreasing Ross risk aversion : higher-order generalizations and implications",
abstract = "We define decreasing higher-degree Ross risk aversion and provide an intuitive interpretation for it. We show that all deteriorations of background risk in the sense of n -th risk increase raise risk aversion in the Arrow-Pratt sense if and only if decreasing ( n + 1 ) -th degree Ross risk aversion holds. Meanwhile, the utility functional form of the agent with decreasing ( n + 1 ) -th degree Ross risk aversion is specified. Our result also implies decreasing 3-rd degree Ross risk aversion can be used to characterize the sufficient condition of risk vulnerability. Moreover, our analysis shows the implication of decreasing n / m -th ( n > m ≥ 1 ) Ross risk aversion.",
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Decreasing Ross risk aversion : higher-order generalizations and implications. / WANG, Jianli; LI, Jingyuan.

In: Journal of Mathematical Economics, Vol. 55, 12.2014, p. 136-142.

Research output: Journal PublicationsJournal Article (refereed)Researchpeer-review

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AU - WANG, Jianli

AU - LI, Jingyuan

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AB - We define decreasing higher-degree Ross risk aversion and provide an intuitive interpretation for it. We show that all deteriorations of background risk in the sense of n -th risk increase raise risk aversion in the Arrow-Pratt sense if and only if decreasing ( n + 1 ) -th degree Ross risk aversion holds. Meanwhile, the utility functional form of the agent with decreasing ( n + 1 ) -th degree Ross risk aversion is specified. Our result also implies decreasing 3-rd degree Ross risk aversion can be used to characterize the sufficient condition of risk vulnerability. Moreover, our analysis shows the implication of decreasing n / m -th ( n > m ≥ 1 ) Ross risk aversion.

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