2022/06/24 by Kim Weston, Weston, Kim · 2 citations
Economics, Econometrics and Finance · #Economic theories and models #Stochastic processes and financial applications #Monetary Policy and Economic Impact
paper · pdf · doi:10.48550/arxiv.2206.12399
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. Our analysis centers around the existence and uniqueness of a solution to a coupled system of quadratic backward stochastic differential equations (BSDEs). We prove that the BSDE system has a unique S^∞\timesbmo solution. We define a candidate equilibrium in terms of the BSDE solution and prove through a verification argument that the candidate is a Radner equilibrium with limited participation. This work generalizes the model of Basak and Cuoco (1998) to allow for a stock with a general dividend stream and agents with exponential preferences. We also provide an explicit example.