A Continuous-Time Utility Maximization Problem with Borrowing Constraints in Macroeconomic Heterogeneous Agent Models: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 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.
Keywords: Continuous-Time Utility Maximization; Borrowing Constraints; Hamilton–Jacobi–Bellman Equation; Viscosity Solution (search for similar items in EconPapers)
JEL-codes: C61 E21 G11 (search for similar items in EconPapers)
Pages: 63
Date: 2022-10
New Economics Papers: this item is included in nep-dge and nep-upt
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Citations: View citations in EconPapers (1)
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Persistent link: https://EconPapers.repec.org/RePEc:kue:epaper:e-22-009
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