A limited participation economy models the real-world phenomenon that some economic agents have access to more of the financial market than others. We prove the global existence of a Radner equilibrium with limited participation, where the agents have exponential preferences and derive utility from both running consumption and terminal wealth. The analysis centers around a coupled, quadratic backward stochastic differential equation (BSDE) system, whose equations describe the economic agents' stochastic control solutions and equilibrium prices. We define a candidate equilibrium in terms of the BSDE system solution and prove through a verification argument that the candidate is a Radner equilibrium with limited participation. Finally, we prove that the BSDE system has a unique $\mathcal{S}^\infty\times\text{bmo}$ solution. This work generalizes the model of Basak and Cuoco (RFS 1998) to allow for a stock with a general dividend stream and agents with stochastic income streams and exponential preferences.

Bio: Kim Weston is an assistant professor of mathematics at Rutgers University in New Jersey, USA. She earned her doctorate at Carnegie Mellon in 2016 under the supervision of Dmitry Kramkov. Kim was an NSF postdoctoral fellow at UT Austin and Rutgers University before joining Rutgers University as an assistant professor. Her research involves the stochastic analysis behind financial economics.