Stochastic analysis of overlapping generations models under incomplete markets
Abstract
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.
Fields of Study & Subjects
Economic theories and models
Stochastic processes and financial applications
Complex Systems and Time Series Analysis
Publication details
- Journal / source
- Mathematics and Financial Economics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 20
- Issue
- 2
- Pages
- 405–453
- Publication date
- 1 June 2026
- Language
- EN