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| Format: | Preprint |
| Publié: |
2021
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| Accès en ligne: | https://arxiv.org/abs/2101.02470 |
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| _version_ | 1866912047370862592 |
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| author | Mayerhofer, Eberhard |
| author_facet | Mayerhofer, Eberhard |
| contents | We establish lower norm bounds for multivariate functions within weighted Lebesgue spaces, characterized by a summation of functions whose components solve a system of nonlinear integral equations. This problem originates in portfolio selection theory, where these equations allow to identify mean-variance optimal portfolios, composed of standard European Options on several underlying assets. We elaborate on the Smirnov property-an integrability condition for the weights that guarantees the uniqueness of solutions to the system. Sufficient conditions on weights to satisfy this property are provided, and counterexamples are constructed, where either the Smirnov property does not hold, or the uniqueness of solutions fails. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_02470 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Smirnov Property for weighted Lebesgue spaces Mayerhofer, Eberhard Functional Analysis 26B35, 52A21, 31B10 We establish lower norm bounds for multivariate functions within weighted Lebesgue spaces, characterized by a summation of functions whose components solve a system of nonlinear integral equations. This problem originates in portfolio selection theory, where these equations allow to identify mean-variance optimal portfolios, composed of standard European Options on several underlying assets. We elaborate on the Smirnov property-an integrability condition for the weights that guarantees the uniqueness of solutions to the system. Sufficient conditions on weights to satisfy this property are provided, and counterexamples are constructed, where either the Smirnov property does not hold, or the uniqueness of solutions fails. |
| title | The Smirnov Property for weighted Lebesgue spaces |
| topic | Functional Analysis 26B35, 52A21, 31B10 |
| url | https://arxiv.org/abs/2101.02470 |