From Semi-Infinite Constraints to Structured Robust Policies: Optimal Gain Selection for Financial Systems
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866913653833334784 |
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| author | Hsieh, Chung-Han |
| author_facet | Hsieh, Chung-Han |
| contents | This paper studies the robust optimal gain selection problem for financial trading systems, formulated within a \emph{double linear policy} framework, which allocates capital across long and short positions. The key objective is to guarantee \emph{robust positive expected} (RPE) profits uniformly across a range of uncertain market conditions while ensuring risk control. This problem leads to a robust optimization formulation with \emph{semi-infinite} constraints, where the uncertainty is modeled by a bounded set of possible return parameters. We address this by transforming semi-infinite constraints into structured policies -- the \emph{balanced} policy and the \emph{complementary} policy -- which enable explicit characterization of the optimal solution. Additionally, we propose a novel graphical approach to efficiently solve the robust gain selection problem, drastically reducing computational complexity. Empirical validation on historical stock price data demonstrates superior performance in terms of risk-adjusted returns and downside risk compared to conventional strategies. This framework generalizes classical mean-variance optimization by incorporating robustness considerations, offering a systematic and efficient solution for robust trading under uncertainty. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2202_02300 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | From Semi-Infinite Constraints to Structured Robust Policies: Optimal Gain Selection for Financial Systems Hsieh, Chung-Han Systems and Control Optimization and Control Computational Finance Mathematical Finance 90C17, 93B35, 93E20, 90C34, 90C15, 91-10, This paper studies the robust optimal gain selection problem for financial trading systems, formulated within a \emph{double linear policy} framework, which allocates capital across long and short positions. The key objective is to guarantee \emph{robust positive expected} (RPE) profits uniformly across a range of uncertain market conditions while ensuring risk control. This problem leads to a robust optimization formulation with \emph{semi-infinite} constraints, where the uncertainty is modeled by a bounded set of possible return parameters. We address this by transforming semi-infinite constraints into structured policies -- the \emph{balanced} policy and the \emph{complementary} policy -- which enable explicit characterization of the optimal solution. Additionally, we propose a novel graphical approach to efficiently solve the robust gain selection problem, drastically reducing computational complexity. Empirical validation on historical stock price data demonstrates superior performance in terms of risk-adjusted returns and downside risk compared to conventional strategies. This framework generalizes classical mean-variance optimization by incorporating robustness considerations, offering a systematic and efficient solution for robust trading under uncertainty. |
| title | From Semi-Infinite Constraints to Structured Robust Policies: Optimal Gain Selection for Financial Systems |
| topic | Systems and Control Optimization and Control Computational Finance Mathematical Finance 90C17, 93B35, 93E20, 90C34, 90C15, 91-10, |
| url | https://arxiv.org/abs/2202.02300 |