Convex ordering for stochastic control: the (path dependent) swing contracts case
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911087561015296 |
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| author | Pagès, Gilles Yeo, Christian |
| author_facet | Pagès, Gilles Yeo, Christian |
| contents | We investigate propagation of convexity and convex ordering on a typical discrete-time stochastic optimal control problem, namely the pricing of swing option. The dynamics of the underlying asset is modelled by the Euler scheme of a Brownian diffusion with affine drift, and convex volatility. We prove that the value function associated to the stochastic optimal control problem is a convex function of the underlying asset price. We also introduce a domination criterion offering insights into the functional monotonicity of the value function with respect to parameters of the underlying dynamics. We particularly focus on the one-dimensional setting where, by means of Stein's formula and regularization techniques, we show that the convexity assumption for the volatility dynamics can be relaxed with a semi-convexity assumption. Finally, to validate our results, we also conduct numerical illustrations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07464 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convex ordering for stochastic control: the (path dependent) swing contracts case Pagès, Gilles Yeo, Christian Mathematical Finance We investigate propagation of convexity and convex ordering on a typical discrete-time stochastic optimal control problem, namely the pricing of swing option. The dynamics of the underlying asset is modelled by the Euler scheme of a Brownian diffusion with affine drift, and convex volatility. We prove that the value function associated to the stochastic optimal control problem is a convex function of the underlying asset price. We also introduce a domination criterion offering insights into the functional monotonicity of the value function with respect to parameters of the underlying dynamics. We particularly focus on the one-dimensional setting where, by means of Stein's formula and regularization techniques, we show that the convexity assumption for the volatility dynamics can be relaxed with a semi-convexity assumption. Finally, to validate our results, we also conduct numerical illustrations. |
| title | Convex ordering for stochastic control: the (path dependent) swing contracts case |
| topic | Mathematical Finance |
| url | https://arxiv.org/abs/2406.07464 |