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| Main Authors: | , |
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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2305.09471 |
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| _version_ | 1866915800447713280 |
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| author | Fießinger, Felix Stadje, Mitja |
| author_facet | Fießinger, Felix Stadje, Mitja |
| contents | Focusing on gains & losses relative to a risk-free benchmark instead of terminal wealth, we consider an asset allocation problem to maximize time-consistently a mean-risk reward function with a general risk measure which is i) law-invariant, ii) cash- or shift-invariant, and iii) positively homogeneous, and possibly plugged into a general function. Examples include (relative) Value at Risk, coherent risk measures, variance, and generalized deviation risk measures. We model the market via a generalized version of the multi-dimensional Black-Scholes model using $α$-stable Lévy processes and give supplementary results for the classical Black-Scholes model. The optimal solution to this problem is a Nash subgame equilibrium given by the solution of an extended Hamilton-Jacobi-Bellman equation. Moreover, we show that the optimal solution is deterministic under appropriate assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_09471 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Time-Consistent Asset Allocation for Risk Measures in a Lévy Market Fießinger, Felix Stadje, Mitja Mathematical Finance Optimization and Control 91B51, 93E20, 60G52, 49L99, 35Q91, 49J20, 46B09 Focusing on gains & losses relative to a risk-free benchmark instead of terminal wealth, we consider an asset allocation problem to maximize time-consistently a mean-risk reward function with a general risk measure which is i) law-invariant, ii) cash- or shift-invariant, and iii) positively homogeneous, and possibly plugged into a general function. Examples include (relative) Value at Risk, coherent risk measures, variance, and generalized deviation risk measures. We model the market via a generalized version of the multi-dimensional Black-Scholes model using $α$-stable Lévy processes and give supplementary results for the classical Black-Scholes model. The optimal solution to this problem is a Nash subgame equilibrium given by the solution of an extended Hamilton-Jacobi-Bellman equation. Moreover, we show that the optimal solution is deterministic under appropriate assumptions. |
| title | Time-Consistent Asset Allocation for Risk Measures in a Lévy Market |
| topic | Mathematical Finance Optimization and Control 91B51, 93E20, 60G52, 49L99, 35Q91, 49J20, 46B09 |
| url | https://arxiv.org/abs/2305.09471 |