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Long-term decomposition of robust pricing kernels under G-expectation

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  • Jaehyun Kim
  • Hyungbin Park

Abstract

This study develops a BSDE method for 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 a solution to a PDE. This study extends previous findings obtained under a single fixed probability framework to the G-expectation context.

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  • Jaehyun Kim & Hyungbin Park, 2024. "Long-term decomposition of robust pricing kernels under G-expectation," Papers 2409.00535, arXiv.org.
    • Handle: RePEc:arx:papers:2409.00535
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    References listed on IDEAS

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    1. Lars Peter Hansen & José A. Scheinkman, 2009. "Long-Term Risk: An Operator Approach," Econometrica, Econometric Society, vol. 77(1), pages 177-234, January.
    2. Osuka, Emi, 2013. "Girsanov’s formula for G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1301-1318.
    3. Lars Peter Hansen, 2012. "Dynamic Valuation Decomposition Within Stochastic Economies," Econometrica, Econometric Society, vol. 80(3), pages 911-967, May.
    4. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
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