Stochastic Analysis of Overlapping Generations Models Under Incomplete Markets

Cangxiong Chen; Sigmund Ellingsrud; Fabian Harang; Alfonso Irarrazabal; Avi Mayorcas

Stochastic Analysis of Overlapping Generations Models Under Incomplete Markets

Cangxiong Chen, Sigmund Ellingsrud, Fabian Harang, Alfonso Irarrazabal, Avi Mayorcas

BI Norwegian Business School

Research output: Working paper / Preprint › Preprint

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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.

Original language	English
Publisher	arXiv
Publication status	Submitted - 5 Sept 2025

Funding

FH gratefully acknowledge the support of the Center for Advanced Studies (CAS) in Oslo, which funded the Signatures for Images project during the academic year 2023/2024, when this work started. AM and CC were supported by EPSRC Mathematical Sciences Small Grant UKRI253: FBSDE Methods in Heterogeneous Agent Models.

Keywords

math.PR
math.OC
91B70, 91B74, 93E20, 65K10

Access to Document

2509.05170v1Submitted manuscript, 22 MBLicence: CC BY

https://arxiv.org/abs/2509.05170Licence: CC BY

FBSDE Methods in Heterogeneous Agent Models
Mayorcas, A. (PI), Pryer, T. (CoI) & Chen, C. (Researcher)
Engineering and Physical Sciences Research Council
25/11/24 → 24/11/25
Project: Research council

Cite this

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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.",

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AU - Chen, Cangxiong

AU - Ellingsrud, Sigmund

AU - Harang, Fabian

AU - Irarrazabal, Alfonso

AU - Mayorcas, Avi

PY - 2025/9/5

Y1 - 2025/9/5

N2 - 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.

AB - 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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KW - math.OC

KW - 91B70, 91B74, 93E20, 65K10

M3 - Preprint

BT - Stochastic Analysis of Overlapping Generations Models Under Incomplete Markets

PB - arXiv

ER -

Stochastic Analysis of Overlapping Generations Models Under Incomplete Markets

Abstract

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Keywords

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Projects

FBSDE Methods in Heterogeneous Agent Models

Cite this