Stochastic Analysis of Overlapping Generations Models Under Incomplete Markets

2025/09/05 by Chen, Cangxiong, Ellingsrud, Sigmund, Harang, Fabian +2 · 1 citation
#65K10 #91B70 #91B74 #93E20 #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2509.05170

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.

Citations

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