A Characterization of the n-th Degree Bounded Stochastic Dominance
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866916012158353408 |
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| author | Light, Bar Perlroth, Andres |
| author_facet | Light, Bar Perlroth, Andres |
| contents | We provide a novel characterization of the $n$-th degree bounded stochastic dominance (BSD) order, linking it to the risk tolerance of decision-makers and providing a decision-theoretic foundation for these stochastic orders. Our results reveal that BSD reflects specific risk preferences through the choice of the interval $[a,b]$, by characterizing it in terms of utility functions with globally bounded Arrow--Pratt risk aversion or that satisfy an $n$-convexity condition. They also highlight limitations of BSD, including its dependence on the chosen support interval and the resulting peculiar risk aversion behavior of decision-makers included in the generator of BSD. To partially address this issue, we use our characterization to separate two roles that are combined in BSD: the largest payoff in the lotteries and the upper endpoint of the interval that determines the Arrow--Pratt lower bound. We then introduce a related lower-partial-moment order that provides a clean trade-off between expected value and downside-risk protection. Using our characterization, we present comparative statics results for decision-making under uncertainty with globally bounded risk aversion measures and savings decisions under globally bounded prudence measures, and derive inequalities for $n$-convex functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_07474 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Characterization of the n-th Degree Bounded Stochastic Dominance Light, Bar Perlroth, Andres Probability We provide a novel characterization of the $n$-th degree bounded stochastic dominance (BSD) order, linking it to the risk tolerance of decision-makers and providing a decision-theoretic foundation for these stochastic orders. Our results reveal that BSD reflects specific risk preferences through the choice of the interval $[a,b]$, by characterizing it in terms of utility functions with globally bounded Arrow--Pratt risk aversion or that satisfy an $n$-convexity condition. They also highlight limitations of BSD, including its dependence on the chosen support interval and the resulting peculiar risk aversion behavior of decision-makers included in the generator of BSD. To partially address this issue, we use our characterization to separate two roles that are combined in BSD: the largest payoff in the lotteries and the upper endpoint of the interval that determines the Arrow--Pratt lower bound. We then introduce a related lower-partial-moment order that provides a clean trade-off between expected value and downside-risk protection. Using our characterization, we present comparative statics results for decision-making under uncertainty with globally bounded risk aversion measures and savings decisions under globally bounded prudence measures, and derive inequalities for $n$-convex functions. |
| title | A Characterization of the n-th Degree Bounded Stochastic Dominance |
| topic | Probability |
| url | https://arxiv.org/abs/2212.07474 |