发表机构
The Chinese University of Hong Kong; Seoul National University（香港中文大学; 首尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在G-期望框架下研究带内生短期利率反馈的稳健债券定价，通过二次G-BSDE建立解的存在唯一性及指数收敛，并应用于逆利率设计与长期限反馈规则构造。
AI 中文摘要
我们在波动率不确定性下研究具有内生短期利率反馈的稳健债券估值。在G-期望框架内，短期利率对债券价格的依赖产生了一个非线性不动点问题，该问题由对数价格所满足的二次G-BSDE表示。在适当假设下，我们建立了有界有限时域解的存在性、唯一性、比较性和稳定性。额外的严格单调性条件可得出唯一的有界无限时域解，以及在紧时间区间上有限时域逼近的指数收敛性。我们将这些结果应用于逆短期利率设计，构造出在固定到期日重现可容许光滑债券价格目标的贴现率系数。对于长期限，我们构造了反馈规则，使得补偿对数价格指数收敛到指定的有界状态依赖轮廓，同时渐近收益率等于指定目标。
英文摘要
We study robust bond valuation with endogenous short-rate feedback under volatility uncertainty. Within the $G$-expectation framework, the dependence of the short rate on the bond price yields a nonlinear fixed-point problem, represented by a quadratic $G$-BSDE for the logarithmic price. Under suitable assumptions, we establish existence, uniqueness, comparison, and stability for bounded finite-horizon solutions. An additional strict monotonicity condition yields a unique bounded infinite-horizon solution and exponential convergence of finite-horizon approximations on compact time intervals. We apply these results to inverse short-rate design, constructing discount-rate coefficients that reproduce admissible smooth bond-price targets at a fixed maturity. For long maturities, we construct feedback rules under which the compensated logarithmic price converges exponentially to a prescribed bounded state-dependent profile, while the asymptotic yield equals a specified target.
