A Consumption-investment Model with State-dependent Lower Bound Constraint on Consumption

Chonghu Guan, Zuo Quan Xu, Fahuai Yi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

6 Citations (Scopus)

Abstract

This paper studies a life-time consumption-investment problem under the Black-Scholes framework, where the consumption rate is subject to a lower bound constraint that linearly depends on the investor's wealth. It is a stochastic control problem with state-dependent control constraint to which the standard stochastic control theory cannot be directly applied. We overcome this by transforming it into an equivalent stochastic control problem in which the control constraint is state-independent so that the standard theory can be applied. We give an explicit optimal consumption-investment strategy when the constraint is homogeneous. When the constraint is non-homogeneous, it is shown that the value function is third-order continuously differentiable by a differential equation approach, and a feedback form optimal consumption-investment strategy is provided. According to our findings, if the investor is concerned with long-term more than short-term consumption, then she should always consume as few as possible; otherwise, she should consume optimally when her wealth is above a threshold, and consume as few as possible when her wealth is below the threshold.

Original languageEnglish
Article number126511
Pages (from-to)1-25
Number of pages25
JournalJournal of Mathematical Analysis and Applications
Volume516
Issue number1
DOIs
Publication statusPublished - 1 Dec 2022

Keywords

  • Dual transformation
  • Dynamic programming
  • Optimal consumption-investment
  • State-dependent constraint
  • Viscosity solution

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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