Math Financ Econ. 2026;20(2):405-453. doi: 10.1007/s11579-026-00418-5. Epub 2026 Aug 1.
ABSTRACT
We provide a stochastic analysis of an overlapping-generations model under incomplete markets. By casting individual optimization with idiosyncratic income risk into a forward-backward stochastic differential-equation (FBSDE) system, we (i) establish existence and uniqueness of the dynamic general-equilibrium interest rate and (ii) derive analytical and semi-explicit formulas for both the equilibrium interest-rate path and the natural borrowing limit – defined as the discounted expected shortfall of future income. Our FBSDE-based approach yields tractable policy functions and equilibrium mappings without relying on high-dimensional PDE methods, offering clear insights into how income dynamics and demographic structure drive interest-rate fluctuations and credit constraints.
PMID:42666272 | PMC:PMC13521973 | DOI:10.1007/s11579-026-00418-5
