Smoothness of the Value Function for Optimal Consumption Model with Consumption-Wealth Utility and Borrowing Constraint

Weidong Tian and Zimu Zhu

Papers from arXiv.org

Abstract: This paper studies an optimal consumption-investment problem for an investor whose instantaneous utility depends on both consumption and wealth, and the investor faces a general borrowing constraint that the investment amount in the risky asset does not exceed an exogenous function of the wealth. We show that the value function is second-order smooth and present the optimal consumption-investment policy in a feedback form. Moreover, when the risky investment amount is bounded above by a fixed constant, we show that under certain conditions, the constraint is binding if and only if an endogenous threshold bounds the portfolio wealth, and we determine the endogenous wealth threshold with the smooth fit condition. Our results encompass several well-developed portfolio choice models and imply new applications.

Date: 2022-10, Revised 2023-12
New Economics Papers: this item is included in nep-dge and nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2210.01016 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2210.01016

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().