Generalized Families of Fractional Stochastic Dominance
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2023
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| _version_ | 1866929711118024704 |
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| author | Azmoodeh, Ehsan Hür, Ozan |
| author_facet | Azmoodeh, Ehsan Hür, Ozan |
| contents | Introduced by Müller et al. in their seminal paper \cite{muller}, fractional stochastic dominance (SD) offers a nuanced approach to ordering distributions. In this paper, we propose a fundamentally new framework by replacing the fixed parameter $γ\in [0,1]$ in fractional SD with a function $\boldsymbolγ: \mathbb{R} \to [0,1]$. This yields two novel families, multi-fractional stochastic dominance (MFSD) and functional fractional stochastic dominance (FFSD). They enable the ranking of a broader range of distributions and incorporate a more informative utility class, including those with local non-concavities whose steepness varies depending on the location. Furthermore, our framework introduces the concept of partial greediness, which dynamically captures how behaviour of decision makers adapts to changes in wealth. We also extend this framework to encompass almost stochastic dominance. We provide the mathematical foundations of our generalized framework and study how it offers a novel tool for ordering distributions across various settings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_08651 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generalized Families of Fractional Stochastic Dominance Azmoodeh, Ehsan Hür, Ozan Mathematical Finance Risk Management Primary 60E15, Secondary 90B50, 91B06, 91B16 Introduced by Müller et al. in their seminal paper \cite{muller}, fractional stochastic dominance (SD) offers a nuanced approach to ordering distributions. In this paper, we propose a fundamentally new framework by replacing the fixed parameter $γ\in [0,1]$ in fractional SD with a function $\boldsymbolγ: \mathbb{R} \to [0,1]$. This yields two novel families, multi-fractional stochastic dominance (MFSD) and functional fractional stochastic dominance (FFSD). They enable the ranking of a broader range of distributions and incorporate a more informative utility class, including those with local non-concavities whose steepness varies depending on the location. Furthermore, our framework introduces the concept of partial greediness, which dynamically captures how behaviour of decision makers adapts to changes in wealth. We also extend this framework to encompass almost stochastic dominance. We provide the mathematical foundations of our generalized framework and study how it offers a novel tool for ordering distributions across various settings. |
| title | Generalized Families of Fractional Stochastic Dominance |
| topic | Mathematical Finance Risk Management Primary 60E15, Secondary 90B50, 91B06, 91B16 |
| url | https://arxiv.org/abs/2307.08651 |