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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/1912.03202 |
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| _version_ | 1866914856474509312 |
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| author | Di Nunno, Giulia Haferkorn, Hannes Khedher, Asma Vanmaele, Michèle |
| author_facet | Di Nunno, Giulia Haferkorn, Hannes Khedher, Asma Vanmaele, Michèle |
| contents | We consider the problem of maximising expected utility from terminal wealth in a semimartingale setting, where the semimartingale is written as a sum of a time-changed Brownian motion and a finite variation process. To solve this problem, we consider an initial enlargement of filtration and we derive change of variable formulas for stochastic integrals w.r.t. a time-changed Brownian motion. The change of variable formulas allow us to shift the problem to a maximisation problem under the enlarged filtration for models driven by a Brownian motion and a finite variation process. The latter could be solved by using martingale methods. Then applying again the change of variable formula, we derive the optimal strategy for the original problem for a power utility under certain assumptions on the finite variation process of the semimartingale. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_03202 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Utility maximisation and time-change Di Nunno, Giulia Haferkorn, Hannes Khedher, Asma Vanmaele, Michèle Probability We consider the problem of maximising expected utility from terminal wealth in a semimartingale setting, where the semimartingale is written as a sum of a time-changed Brownian motion and a finite variation process. To solve this problem, we consider an initial enlargement of filtration and we derive change of variable formulas for stochastic integrals w.r.t. a time-changed Brownian motion. The change of variable formulas allow us to shift the problem to a maximisation problem under the enlarged filtration for models driven by a Brownian motion and a finite variation process. The latter could be solved by using martingale methods. Then applying again the change of variable formula, we derive the optimal strategy for the original problem for a power utility under certain assumptions on the finite variation process of the semimartingale. |
| title | Utility maximisation and time-change |
| topic | Probability |
| url | https://arxiv.org/abs/1912.03202 |