Examples and Counterexamples of Cost-efficiency in Incomplete Markets
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916320306528256 |
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| author | Bernard, Carole Sturm, Stephan |
| author_facet | Bernard, Carole Sturm, Stephan |
| contents | We present a number of examples and counterexamples to illustrate the results on cost-efficiency in an incomplete market obtained in [BS24]. These examples and counterexamples do not only illustrate the results obtained in [BS24], but show the limitations of the results and the sharpness of the key assumptions. In particular, we make use of a simple 3-state model in which we are able to recover and illustrate all key results of the paper. This example also shows how our characterization of perfectly cost-efficient claims allows to solve an expected utility maximization problem in a simple incomplete market (trinomial model) and recover results from [DS06, Chapter 3], there obtained using duality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08756 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Examples and Counterexamples of Cost-efficiency in Incomplete Markets Bernard, Carole Sturm, Stephan Computer Science and Game Theory Probability Mathematical Finance Portfolio Management 91G10, 60E15, 90B50 We present a number of examples and counterexamples to illustrate the results on cost-efficiency in an incomplete market obtained in [BS24]. These examples and counterexamples do not only illustrate the results obtained in [BS24], but show the limitations of the results and the sharpness of the key assumptions. In particular, we make use of a simple 3-state model in which we are able to recover and illustrate all key results of the paper. This example also shows how our characterization of perfectly cost-efficient claims allows to solve an expected utility maximization problem in a simple incomplete market (trinomial model) and recover results from [DS06, Chapter 3], there obtained using duality. |
| title | Examples and Counterexamples of Cost-efficiency in Incomplete Markets |
| topic | Computer Science and Game Theory Probability Mathematical Finance Portfolio Management 91G10, 60E15, 90B50 |
| url | https://arxiv.org/abs/2407.08756 |