A G-BSDE approach to the long-term decomposition of robust pricing kernels
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908491189321728 |
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| author | Kim, Jaehyun Park, Hyungbin |
| author_facet | Kim, Jaehyun Park, Hyungbin |
| contents | This study proposes a BSDE approach to the long-term decomposition of pricing kernels under the G-expectation framework. We establish the existence, uniqueness, and regularity of solutions to three types of quadratic G-BSDEs: finite-horizon G-BSDEs, infinite-horizon G-BSDEs, and ergodic G-BSDEs. Moreover, we explore the Feynman--Kac formula associated with these three types of quadratic G-BSDEs. Using these results, a pricing kernel is uniquely decomposed into four components: an exponential discounting component, a transitory component, a symmetric G-martingale, and a decreasing component that captures the volatility uncertainty of the G-Brownian motion. Furthermore, these components are represented through the solution to a second-order PDE. This study extends previous findings obtained under a single fixed probability framework to the G-expectation context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00535 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A G-BSDE approach to the long-term decomposition of robust pricing kernels Kim, Jaehyun Park, Hyungbin Mathematical Finance This study proposes a BSDE approach to the long-term decomposition of pricing kernels under the G-expectation framework. We establish the existence, uniqueness, and regularity of solutions to three types of quadratic G-BSDEs: finite-horizon G-BSDEs, infinite-horizon G-BSDEs, and ergodic G-BSDEs. Moreover, we explore the Feynman--Kac formula associated with these three types of quadratic G-BSDEs. Using these results, a pricing kernel is uniquely decomposed into four components: an exponential discounting component, a transitory component, a symmetric G-martingale, and a decreasing component that captures the volatility uncertainty of the G-Brownian motion. Furthermore, these components are represented through the solution to a second-order PDE. This study extends previous findings obtained under a single fixed probability framework to the G-expectation context. |
| title | A G-BSDE approach to the long-term decomposition of robust pricing kernels |
| topic | Mathematical Finance |
| url | https://arxiv.org/abs/2409.00535 |