Indexing gamble desirability by extending proportional stochastic dominance

We characterise two new orders of desirability of gambles (risky assets) that are natural extensions of the stochastic dominance order to complete orders, based on choosing optimal proportions of gambles. These orders are represented by indices, which we term the S index and the G index, that are ch...

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Bibliographic Details
Published inGames and economic behavior Vol. 109; pp. 523 - 543
Main Authors Hellman, Ziv, Schreiber, Amnon
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.05.2018
Subjects
Absolute risk
Indices of riskiness
Relative risk
Risk aversion
Risk aversion
D81
Indices of riskiness
G32
Absolute risk
Relative risk
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Summary:We characterise two new orders of desirability of gambles (risky assets) that are natural extensions of the stochastic dominance order to complete orders, based on choosing optimal proportions of gambles. These orders are represented by indices, which we term the S index and the G index, that are characterised axiomatically and by wealth and utility uniform dominance concepts. The S index can be viewed as a generalised Sharpe ratio, and the G index can be used for maximising the growth path of a portfolio. •We characterise two new risk orders that complete the stochastic dominance order.•These are based on choosing optimal proportions of gambles.•The S index generalises the Sharpe ratio.•The G index can be used for maximising the growth path of a portfolio.•Either one may serve as reasonable objective functions for investment.
ISSN:0899-8256
1090-2473
DOI:10.1016/j.geb.2018.02.003