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A Continuous-Time Utility Maximization Problem with Borrowing Constraints in Macroeconomic Heterogeneous Agent Models:A Case of Regular Controls under Markov Chain Uncertainty

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  • Yuki SHIGETA

Abstract

This paper is concerned with the verification of a continuous-time utility max- imization problem frequently used in recent macroeconomics. By focusing on Markov chain uncertainty, the problem in this paper can feature many charac- teristics of a typical consumer’s problem in macroeconomics, such as borrowing constraints, endogenous labor supply, unhedgeable labor income, multiple asset choice, stochastic changes in preference, and others. I show that the value func- tion of the problem is actually a constrained viscosity solution to the associated Hamilton–Jacobi–Bellman equation. Furthermore, the value function is continu- ously differentiable in the interior of its domain. Finally, the candidate optimal control is admissible, unique, and actually optimal.

Suggested Citation

  • 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.
    • Handle: RePEc:kue:epaper:e-22-009
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    1. 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.

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    More about this item

    Keywords

    Continuous-Time Utility Maximization; Borrowing Constraints; Hamilton–Jacobi–Bellman Equation; Viscosity Solution;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • 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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