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arXiv · 2509.05170

Stochastic Analysis of Overlapping Generations Models Under Incomplete Markets

Cangxiong Chen·Sigmund Ellingsrud·Fabian Harang·Alfonso Irarrazabal·Avi Mayorcas
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Abstract

We provide a stochastic analysis of an overlapping-generations model under incomplete markets. By casting individual optimisation with idiosyncratic income risk into a forward-backward stochastic differential equation (FBSDE) system, we (i) establish existence and uniqueness of the dynamic general-equilibirum interest rate and (ii) derive 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 intereate-rate fluctuations and credit constraints.

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Cangxiong Chen, Sigmund Ellingsrud, Fabian Harang, Alfonso Irarrazabal, Avi Mayorcas. 2025-09-05. Stochastic Analysis of Overlapping Generations Models Under Incomplete Markets. https://arxiv.org/abs/2509.05170

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