Existence of an equilibrium with limited participation

Kim Weston ()
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Kim Weston: Rutgers University

Finance and Stochastics, 2024, vol. 28, issue 2, No 2, 329-361

Abstract: 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 S ∞ × bmo ${\mathcal{S}}^{\infty }\times \text{bmo}$ . 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.

Keywords: Incomplete Radner equilibrium; Limited participation; Multidimensional BSDE; Diagonally quadratic generator; BMO-martingale; 60G99; 60H30; 91B70; 91G80 (search for similar items in EconPapers)
JEL-codes: D52 G12 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00780-024-00530-8

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