English, Article, Journal or magazine article edition: Duality Mappings For The Theory of Risk Aversion with Vector Outcomes Sudhir A. Shah

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Physical Description
  • preprint
Language
  • English

Edition details

Title
  • Duality mappings for the theory of risk aversion with vector outcomes
Author
  • Sudhir A. Shah
Physical Description
  • preprint
Notes
  • The Author considera a decision-making environment with an outcome space that is a convex and compact subset of a vector space belonging to a general class of such spaces. Given this outcome space,he defines general classes of (a) risk averse von Neumann-Morgenstern utility functions defined over the outcome space, (b) multi-valued mappings that yield the certainty equivalent outcomes corresponding to a lottery, (c) multi-valued mappings that yield the risk premia corresponding to a lottery, and (d) multi-valued mappings that yield the acceptance set of lotteries corresponding to an outcome. Their duality results establish that the usual mappings that generate (b), (c) and (d) from (a) are bijective.They apply these results to the problem of computing the value of financial assets to a risk averse decision-maker and show that this value will always be less than the arbitrage-free valuation.[CDS WP NO 160]
  • RePEc:ess:wpaper:id:2085
  • We consider a decision-making environment with an outcome space that is a convex and compact subset of a vector space belonging to a general class of such spaces. Given this outcome space, we de¯ne gen- eral classes of (a) risk averse von Neumann-Morgenstern utility func- tions de¯ned over the outcome space, (b) multi-valued mappings that yield the certainty equivalent outcomes corresponding to a lottery, (c) multi-valued mappings that yield the risk premia corresponding to a lottery, and (d) multi-valued mappings that yield the acceptance set of lotteries corresponding to an outcome. Our duality results establish that the usual mappings that generate (b), (c) and (d) from (a) are bi- jective. We apply these results to the problem of computing the value of ¯nancial assets to a risk averse decision-maker and show that this value will always be less than the arbitrage-free valuation.
  • Risk aversion, vector outcomes, certainty equivalence, risk premia, acceptance set
  • RePEc:cde:cdewps:160
Language
  • English
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