A Martingale approach to continuous Portfolio Optimization under CVaR like constraints
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911185800003584 |
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| author | Lelong, Jérôme Maume-Deschamps, Véronique Thevenot, William |
| author_facet | Lelong, Jérôme Maume-Deschamps, Véronique Thevenot, William |
| contents | We study a continuous-time portfolio optimization problem under an explicit constraint on the Deviation Conditional Value-at-Risk (DCVaR), defined as the difference between the CVaR and the expected terminal wealth. While the mean-CVaR framework has been widely explored, its time-inconsistency complicates the use of dynamic programming. We follow the martingale approach in a complete market setting, as in Gao et al. [4], and extend it by retaining an explicit DCVaR constraint in the problem formulation. The optimal terminal wealth is obtained by solving a convex constrained minimization problem. This leads to a tractable and interpretable characterization of the optimal strategy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_26009 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Martingale approach to continuous Portfolio Optimization under CVaR like constraints Lelong, Jérôme Maume-Deschamps, Véronique Thevenot, William Optimization and Control Statistics Theory Risk Management We study a continuous-time portfolio optimization problem under an explicit constraint on the Deviation Conditional Value-at-Risk (DCVaR), defined as the difference between the CVaR and the expected terminal wealth. While the mean-CVaR framework has been widely explored, its time-inconsistency complicates the use of dynamic programming. We follow the martingale approach in a complete market setting, as in Gao et al. [4], and extend it by retaining an explicit DCVaR constraint in the problem formulation. The optimal terminal wealth is obtained by solving a convex constrained minimization problem. This leads to a tractable and interpretable characterization of the optimal strategy. |
| title | A Martingale approach to continuous Portfolio Optimization under CVaR like constraints |
| topic | Optimization and Control Statistics Theory Risk Management |
| url | https://arxiv.org/abs/2509.26009 |