A G-BSDE approach to the long-term decomposition of robust pricing kernels

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Kim, Jaehyun, Park, Hyungbin
Natura: Preprint
Pubblicazione: 2024
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866908491189321728
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