Risk Budgeting Allocation for Dynamic Risk Measures
Fuente:
arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909373475848192 |
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| author | Pesenti, Silvana M. Jaimungal, Sebastian Saporito, Yuri F. Targino, Rodrigo S. |
| author_facet | Pesenti, Silvana M. Jaimungal, Sebastian Saporito, Yuri F. Targino, Rodrigo S. |
| contents | We define and develop an approach for risk budgeting allocation - a risk diversification portfolio strategy - where risk is measured using a dynamic time-consistent risk measure. For this, we introduce a notion of dynamic risk contributions that generalise the classical Euler contributions and which allow us to obtain dynamic risk contributions in a recursive manner. We prove that, for the class of coherent dynamic distortion risk measures, the risk allocation problem may be recast as a sequence of strictly convex optimisation problems. Moreover, we show that self-financing dynamic risk budgeting strategies with initial wealth of 1 are scaled versions of the solution of the sequence of convex optimisation problems. Furthermore, we develop an actor-critic approach, leveraging the elicitability of dynamic risk measures, to solve for risk budgeting strategies using deep learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_11319 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Risk Budgeting Allocation for Dynamic Risk Measures Pesenti, Silvana M. Jaimungal, Sebastian Saporito, Yuri F. Targino, Rodrigo S. Mathematical Finance Portfolio Management Risk Management We define and develop an approach for risk budgeting allocation - a risk diversification portfolio strategy - where risk is measured using a dynamic time-consistent risk measure. For this, we introduce a notion of dynamic risk contributions that generalise the classical Euler contributions and which allow us to obtain dynamic risk contributions in a recursive manner. We prove that, for the class of coherent dynamic distortion risk measures, the risk allocation problem may be recast as a sequence of strictly convex optimisation problems. Moreover, we show that self-financing dynamic risk budgeting strategies with initial wealth of 1 are scaled versions of the solution of the sequence of convex optimisation problems. Furthermore, we develop an actor-critic approach, leveraging the elicitability of dynamic risk measures, to solve for risk budgeting strategies using deep learning. |
| title | Risk Budgeting Allocation for Dynamic Risk Measures |
| topic | Mathematical Finance Portfolio Management Risk Management |
| url | https://arxiv.org/abs/2305.11319 |