Reinforcement Learning for Jump-Diffusions, with Financial Applications
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| Format: | Preprint |
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2024
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| author | Gao, Xuefeng Li, Lingfei Zhou, Xun Yu |
| author_facet | Gao, Xuefeng Li, Lingfei Zhou, Xun Yu |
| contents | We study continuous-time reinforcement learning (RL) for stochastic control in which system dynamics are governed by jump-diffusion processes. We formulate an entropy-regularized exploratory control problem with stochastic policies to capture the exploration--exploitation balance essential for RL. Unlike the pure diffusion case initially studied by Wang et al. (2020), the derivation of the exploratory dynamics under jump-diffusions calls for a careful formulation of the jump part. Through a theoretical analysis, we find that one can simply use the same policy evaluation and $q$-learning algorithms in Jia and Zhou (2022a, 2023), originally developed for controlled diffusions, without needing to check a priori whether the underlying data come from a pure diffusion or a jump-diffusion. However, we show that the presence of jumps ought to affect parameterizations of actors and critics in general. We investigate as an application the mean--variance portfolio selection problem with stock price modelled as a jump-diffusion, and show that both RL algorithms and parameterizations are invariant with respect to jumps. Finally, we present a detailed study on applying the general theory to option hedging. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_16449 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reinforcement Learning for Jump-Diffusions, with Financial Applications Gao, Xuefeng Li, Lingfei Zhou, Xun Yu Machine Learning Optimization and Control Mathematical Finance We study continuous-time reinforcement learning (RL) for stochastic control in which system dynamics are governed by jump-diffusion processes. We formulate an entropy-regularized exploratory control problem with stochastic policies to capture the exploration--exploitation balance essential for RL. Unlike the pure diffusion case initially studied by Wang et al. (2020), the derivation of the exploratory dynamics under jump-diffusions calls for a careful formulation of the jump part. Through a theoretical analysis, we find that one can simply use the same policy evaluation and $q$-learning algorithms in Jia and Zhou (2022a, 2023), originally developed for controlled diffusions, without needing to check a priori whether the underlying data come from a pure diffusion or a jump-diffusion. However, we show that the presence of jumps ought to affect parameterizations of actors and critics in general. We investigate as an application the mean--variance portfolio selection problem with stock price modelled as a jump-diffusion, and show that both RL algorithms and parameterizations are invariant with respect to jumps. Finally, we present a detailed study on applying the general theory to option hedging. |
| title | Reinforcement Learning for Jump-Diffusions, with Financial Applications |
| topic | Machine Learning Optimization and Control Mathematical Finance |
| url | https://arxiv.org/abs/2405.16449 |