Existence of Invariant Measure and Stationary Equilibrium in aContinuous-Time One-Asset Aiyagari Model:A Case of Regular Controls under Markov Chain Uncertainty

Yuki Shigeta

Discussion papers from Graduate School of Economics , Kyoto University

Abstract: This paper is concerned with the existence of the invariant measure and stationary equilibrium in a continuous-time Aiyagari model with an endogenous labor supply. First, I demonstrate that the value function, optimal consumption, optimal labor supply, optimal saving rate, and optimally controlled liquid asset process are jointly continuous in parameters such as the interest rate and wage. Second, I show the existence of the ergodic invariant measure of the optimally controlled liquid asset process. Finally, I demonstrate the existence of the stationary equilibrium in a continuous-time one-asset Aiyagari model.

Keywords: Macroeconomic Mean Field Game; Borrowing Constraint; Hamilton–Jacobi–Bellman Equation; Viscosity Solution; Continuity in Parameters; Existence of Invariant Measure (search for similar items in EconPapers)
JEL-codes: C62 E21 G11 (search for similar items in EconPapers)
Pages: 63
Date: 2022-10
New Economics Papers: this item is included in nep-dge
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:kue:epaper:e-22-010

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