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

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  • Yuki SHIGETA

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.

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  • Yuki SHIGETA, 2022. "Existence of Invariant Measure and Stationary Equilibrium in aContinuous-Time One-Asset Aiyagari Model:A Case of Regular Controls under Markov Chain Uncertainty," Discussion papers e-22-010, Graduate School of Economics , Kyoto University.
    • Handle: RePEc:kue:epaper:e-22-010
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    10. Yuki SHIGETA, 2022. "A Continuous-Time Utility Maximization Problem with Borrowing Constraints in Macroeconomic Heterogeneous Agent Models:A Case of Regular Controls under Markov Chain Uncertainty," Discussion papers e-22-009, Graduate School of Economics , Kyoto University.
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    Cited by:

    1. Yuki SHIGETA, 2022. "A Continuous-Time Utility Maximization Problem with Borrowing Constraints in Macroeconomic Heterogeneous Agent Models:A Case of Regular Controls under Markov Chain Uncertainty," Discussion papers e-22-009, Graduate School of Economics , Kyoto University.

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    More about this item

    Keywords

    Macroeconomic Mean Field Game; Borrowing Constraint; Hamilton–Jacobi–Bellman Equation; Viscosity Solution; Continuity in Parameters; Existence of Invariant Measure;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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