{"ID":2874282,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.05170","arxiv_id":"2509.05170","title":"Stochastic Analysis of Overlapping Generations Models Under Incomplete Markets","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.","short_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...","url_abs":"https://arxiv.org/abs/2509.05170","url_pdf":"https://arxiv.org/pdf/2509.05170v1","authors":"[\"Cangxiong Chen\",\"Sigmund Ellingsrud\",\"Fabian Harang\",\"Alfonso Irarrazabal\",\"Avi Mayorcas\"]","published":"2025-09-05T15:12:58Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.OC\"]","methods":"[]","has_code":false}