Singular Control in a Cash Management Model with Ambiguity
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866918108864708608 |
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| author | Archankul, Arnon Ferrari, Giorgio Hellmann, Tobias Thijssen, Jacco J. J. |
| author_facet | Archankul, Arnon Ferrari, Giorgio Hellmann, Tobias Thijssen, Jacco J. J. |
| contents | We consider a singular control model of cash reserve management, driven by a diffusion under ambiguity. The manager is assumed to have maxmin preferences over a set of priors characterized by $κ$-ignorance. A verification theorem is established to determine the firm's cost function and the optimal cash policy; the latter taking the form of a control barrier policy. In a model driven by arithmetic Brownian motion, we use Dynkin games to show that an increase in ambiguity leads to higher expected costs under the worst-case prior and a narrower inaction region. The latter effect can be used to provide an ambiguity-driven explanation for observed cash management behavior. Our findings can be applied to broader applications of singular control in managing inventories under ambiguity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_12014 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Singular Control in a Cash Management Model with Ambiguity Archankul, Arnon Ferrari, Giorgio Hellmann, Tobias Thijssen, Jacco J. J. Risk Management Optimization and Control Mathematical Finance We consider a singular control model of cash reserve management, driven by a diffusion under ambiguity. The manager is assumed to have maxmin preferences over a set of priors characterized by $κ$-ignorance. A verification theorem is established to determine the firm's cost function and the optimal cash policy; the latter taking the form of a control barrier policy. In a model driven by arithmetic Brownian motion, we use Dynkin games to show that an increase in ambiguity leads to higher expected costs under the worst-case prior and a narrower inaction region. The latter effect can be used to provide an ambiguity-driven explanation for observed cash management behavior. Our findings can be applied to broader applications of singular control in managing inventories under ambiguity. |
| title | Singular Control in a Cash Management Model with Ambiguity |
| topic | Risk Management Optimization and Control Mathematical Finance |
| url | https://arxiv.org/abs/2309.12014 |