1. Existence of an equilibrium with limited participation.
- Author
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Weston, Kim
- Subjects
STOCHASTIC differential equations ,EQUILIBRIUM ,DIVIDENDS ,PARTICIPATION ,THERMODYNAMIC control ,LONG-distance running - 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 . 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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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