Scaling Limits for Exponential Hedging in the Brownian Framework
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866908519418036224 |
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| author | Dolinksy, Yan Zhang, Xin |
| author_facet | Dolinksy, Yan Zhang, Xin |
| contents | In this paper, we consider scaling limits of exponential utility indifference prices for European contingent claims in the Bachelier model. We show that the scaling limit can be represented in terms of the \emph{specific relative entropy}, and in addition we construct asymptotic optimal hedging strategies. To prove the upper bound for the limit, we formulate the dual problem as a stochastic control, and show there exists a classical solution to its Hamilton-Jacobi-Bellman (HJB) equation. The proof for the lower bound relies on the duality result for exponential hedging in discrete time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17186 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scaling Limits for Exponential Hedging in the Brownian Framework Dolinksy, Yan Zhang, Xin Probability Optimization and Control Mathematical Finance Pricing of Securities In this paper, we consider scaling limits of exponential utility indifference prices for European contingent claims in the Bachelier model. We show that the scaling limit can be represented in terms of the \emph{specific relative entropy}, and in addition we construct asymptotic optimal hedging strategies. To prove the upper bound for the limit, we formulate the dual problem as a stochastic control, and show there exists a classical solution to its Hamilton-Jacobi-Bellman (HJB) equation. The proof for the lower bound relies on the duality result for exponential hedging in discrete time. |
| title | Scaling Limits for Exponential Hedging in the Brownian Framework |
| topic | Probability Optimization and Control Mathematical Finance Pricing of Securities |
| url | https://arxiv.org/abs/2502.17186 |