Paper: arXiv 2409.00535

Authors: Jaehyun Kim, Hyungbin Park

Abstract

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.

Complexity vs Empirical Score

  • Math Complexity: 9.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a highly sophisticated theoretical framework extending long-term pricing kernel decompositions to the G-expectation framework using quadratic G-BSDEs and PDEs. While mathematically rigorous and novel in its field, it is purely theoretical with no empirical data analysis, backtesting, or code implementation provided.

Research Flowchart

  flowchart TD
    A[Research Goal: Long-term decomposition of pricing kernels under G-expectation with volatility uncertainty] --> B[Inputs: Multi-asset market dynamics & G-Brownian motion framework]
    B --> C[Establish Existence, Uniqueness & Regularity for Quadratic G-BSDEs]
    
    C --> D1[Finite-Horizon G-BSDEs]
    C --> D2[Infinite-Horizon G-BSDEs]
    C --> D3[Ergodic G-BSDEs]
    
    D1 & D2 & D3 --> E[Derive Nonlinear Feynman-Kac Formulas via 2nd-Order PDEs]
    
    E --> F[Outcome: Unique 4-Component Decomposition of Pricing Kernel]
    
    F --> G1[Exponential Discounting]
    F --> G2[Transitory Component]
    F --> G3[Symmetric G-Martingale]
    F --> G4[Decreasing Component Volatility Uncertainty]

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0 of 37 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.