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<p>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.</p>

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Stochastic analysis of overlapping generations models under incomplete markets

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年8月1日

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  • Cangxiong Chen,
  • Sigmund Ellingsrud,
  • Fabian N. Harang,
  • Alfonso Irarrazabal,
  • Avi Mayorcas

摘要

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.