Quadratic G-BSDEs for bond pricing with endogenous short-rate feedback

RESUMO

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 of bounded finite-horizon solutions. An additional strict monotonicity condition yields a unique bounded infinite-horizon solution with exponential convergence of 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.