Sensitivity of robust optimization problems under drift and volatility uncertainty
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866909506980544512 |
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| author | Bartl, Daniel Neufeld, Ariel Park, Kyunghyun |
| author_facet | Bartl, Daniel Neufeld, Ariel Park, Kyunghyun |
| contents | We examine optimization problems in which an investor has the opportunity to trade in $d$ stocks with the goal of maximizing her worst-case cost of cumulative gains and losses. Here, worst-case refers to taking into account all possible drift and volatility processes for the stocks that fall within a $\varepsilon$-neighborhood of predefined fixed baseline processes. Although solving the worst-case problem for a fixed $\varepsilon>0$ is known to be very challenging in general, we show that it can be approximated as $\varepsilon\to 0$ by the baseline problem (computed using the baseline processes) in the following sense: Firstly, the value of the worst-case problem is equal to the value of the baseline problem plus $\varepsilon$ times a correction term. This correction term can be computed explicitly and quantifies how sensitive a given optimization problem is to model uncertainty. Moreover, approximately optimal trading strategies for the worst-case problem can be obtained using optimal strategies from the corresponding baseline problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_11248 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sensitivity of robust optimization problems under drift and volatility uncertainty Bartl, Daniel Neufeld, Ariel Park, Kyunghyun Optimization and Control Probability Mathematical Finance We examine optimization problems in which an investor has the opportunity to trade in $d$ stocks with the goal of maximizing her worst-case cost of cumulative gains and losses. Here, worst-case refers to taking into account all possible drift and volatility processes for the stocks that fall within a $\varepsilon$-neighborhood of predefined fixed baseline processes. Although solving the worst-case problem for a fixed $\varepsilon>0$ is known to be very challenging in general, we show that it can be approximated as $\varepsilon\to 0$ by the baseline problem (computed using the baseline processes) in the following sense: Firstly, the value of the worst-case problem is equal to the value of the baseline problem plus $\varepsilon$ times a correction term. This correction term can be computed explicitly and quantifies how sensitive a given optimization problem is to model uncertainty. Moreover, approximately optimal trading strategies for the worst-case problem can be obtained using optimal strategies from the corresponding baseline problem. |
| title | Sensitivity of robust optimization problems under drift and volatility uncertainty |
| topic | Optimization and Control Probability Mathematical Finance |
| url | https://arxiv.org/abs/2311.11248 |