Levy-stable scaling of risk and performance functionals
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912701322625024 |
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| author | Vlasiuk, Dmitrii |
| author_facet | Vlasiuk, Dmitrii |
| contents | We develop a finite-horizon model in which liquid-asset returns exhibit Levy-stable scaling on a data-driven window [tau_UV, tau_IR] and aggregate into a finite-variance regime outside. The window and the tail index alpha are identified from the log-log slope of the central body and a two-segment fit of scale versus horizon. With an anchor horizon tau_0, we derive horizon-correct formulas for Value-at-Risk, Expected Shortfall, Sharpe and Information ratios, Kelly under a Value-at-Risk constraint, and one-step drawdown, where each admits a closed-form Gaussian-bias term driven by the exponent gap (1/alpha - 1/2). The implementation is nonparametric up to alpha and fixed tail quantiles. The formulas are reproducible across horizons on the Levy window. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07834 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Levy-stable scaling of risk and performance functionals Vlasiuk, Dmitrii Mathematical Finance Computational Finance Portfolio Management Risk Management Statistical Finance 91G80 We develop a finite-horizon model in which liquid-asset returns exhibit Levy-stable scaling on a data-driven window [tau_UV, tau_IR] and aggregate into a finite-variance regime outside. The window and the tail index alpha are identified from the log-log slope of the central body and a two-segment fit of scale versus horizon. With an anchor horizon tau_0, we derive horizon-correct formulas for Value-at-Risk, Expected Shortfall, Sharpe and Information ratios, Kelly under a Value-at-Risk constraint, and one-step drawdown, where each admits a closed-form Gaussian-bias term driven by the exponent gap (1/alpha - 1/2). The implementation is nonparametric up to alpha and fixed tail quantiles. The formulas are reproducible across horizons on the Levy window. |
| title | Levy-stable scaling of risk and performance functionals |
| topic | Mathematical Finance Computational Finance Portfolio Management Risk Management Statistical Finance 91G80 |
| url | https://arxiv.org/abs/2511.07834 |