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Existence of an equilibrium with limited participation

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Abstract

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 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 solution in \({\mathcal{S}}^{\infty }\times \text{bmo}\). This work generalises the model of Basak and Cuoco (Rev. Financ. Stud. 11:309–341, 1998) to allow a stock with a general dividend stream and agents with stochastic income streams and exponential preferences. We also provide an explicit example.

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  1. Department of Mathematics, Rutgers University, Piscataway, NJ, 08854, USA

    Kim Weston

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  1. Kim Weston
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Correspondence to Kim Weston.

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The author wishes to thank the Associate Editor and anonymous referees for their suggestions and improvements. The author acknowledges support by the National Science Foundation under Grant No. DMS#1908255 (2019-2023). Any opinions, findings and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation (NSF).

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Weston, K. Existence of an equilibrium with limited participation. Finance Stoch 28, 329–361 (2024). https://doi.org/10.1007/s00780-024-00530-8

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