Stochastic dominance for linear combinations of infinite-mean risks
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913819151826944 |
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| author | Chen, Yuyu Hu, Taizhong Shneer, Seva Zou, Zhenfeng |
| author_facet | Chen, Yuyu Hu, Taizhong Shneer, Seva Zou, Zhenfeng |
| contents | In this paper, we establish a sufficient condition to compare linear combinations of independent and identically distributed (iid) infinite-mean random variables under usual stochastic order. We introduce a new class of distributions that includes many commonly used heavy-tailed distributions and show that within this class, a linear combination of random variables is stochastically larger when its weight vector is smaller in the sense of majorization order. We proceed to study the case where each random variable is a compound Poisson sum and demonstrate that if the stochastic dominance relation holds, the summand of the compound Poisson sum belongs to our new class of distributions. Additional discussions are presented for stable distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01739 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic dominance for linear combinations of infinite-mean risks Chen, Yuyu Hu, Taizhong Shneer, Seva Zou, Zhenfeng Probability Risk Management In this paper, we establish a sufficient condition to compare linear combinations of independent and identically distributed (iid) infinite-mean random variables under usual stochastic order. We introduce a new class of distributions that includes many commonly used heavy-tailed distributions and show that within this class, a linear combination of random variables is stochastically larger when its weight vector is smaller in the sense of majorization order. We proceed to study the case where each random variable is a compound Poisson sum and demonstrate that if the stochastic dominance relation holds, the summand of the compound Poisson sum belongs to our new class of distributions. Additional discussions are presented for stable distributions. |
| title | Stochastic dominance for linear combinations of infinite-mean risks |
| topic | Probability Risk Management |
| url | https://arxiv.org/abs/2505.01739 |