Risk-Averse Markov Decision Processes through a Distributional Lens
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866914765991837696 |
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| author | Cheng, Ziteng Jaimungal, Sebastian |
| author_facet | Cheng, Ziteng Jaimungal, Sebastian |
| contents | By adopting a distributional viewpoint on law-invariant convex risk measures, we construct dynamics risk measures (DRMs) at the distributional level. We then apply these DRMs to investigate Markov decision processes, incorporating latent costs, random actions, and weakly continuous transition kernels. Furthermore, the proposed DRMs allow risk aversion to change dynamically. Under mild assumptions, we derive a dynamic programming principle and show the existence of an optimal policy in both finite and infinite time horizons. Moreover, we provide a sufficient condition for the optimality of deterministic actions. For illustration, we conclude the paper with examples from optimal liquidation with limit order books and autonomous driving. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2203_09612 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Risk-Averse Markov Decision Processes through a Distributional Lens Cheng, Ziteng Jaimungal, Sebastian Optimization and Control Mathematical Finance Risk Management By adopting a distributional viewpoint on law-invariant convex risk measures, we construct dynamics risk measures (DRMs) at the distributional level. We then apply these DRMs to investigate Markov decision processes, incorporating latent costs, random actions, and weakly continuous transition kernels. Furthermore, the proposed DRMs allow risk aversion to change dynamically. Under mild assumptions, we derive a dynamic programming principle and show the existence of an optimal policy in both finite and infinite time horizons. Moreover, we provide a sufficient condition for the optimality of deterministic actions. For illustration, we conclude the paper with examples from optimal liquidation with limit order books and autonomous driving. |
| title | Risk-Averse Markov Decision Processes through a Distributional Lens |
| topic | Optimization and Control Mathematical Finance Risk Management |
| url | https://arxiv.org/abs/2203.09612 |