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Updated: Aug 30, 2026

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
Stochastic analysis of overlapping generations models under incomplete markets
Cangxiong Chen1, Sigmund Ellingsrud2, Fabian N Harang2
1School of Computer Science and Statistics, Trinity College Dublin, D02 N8P5 Dublin, Ireland.
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.
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