Optimal consumption with reference to past spending maximum

Shuoqing Deng (), Xun Li (), Huyên Pham () and Xiang Yu ()
Additional contact information
Shuoqing Deng: University of Michigan
Xun Li: The Hong Kong Polytechnic University
Huyên Pham: Université de Paris and CREST-ENSAE
Xiang Yu: The Hong Kong Polytechnic University

Finance and Stochastics, 2022, vol. 26, issue 2, No 3, 217-266

Abstract: Abstract This paper studies the infinite-horizon optimal consumption problem with a path-dependent reference under exponential utility. The performance is measured by the difference between the nonnegative consumption rate and a fraction of the historical consumption maximum. The consumption running maximum process is chosen as an auxiliary state process, and hence the value function depends on two state variables. The Hamilton–Jacobi–Bellman (HJB) equation can be heuristically expressed in a piecewise manner across different regions to take into account all constraints. By employing the dual transform and smooth-fit principle, some thresholds of the wealth variable are derived such that a classical solution to the HJB equation and feedback optimal investment and consumption strategies can be obtained in closed form in each region. A complete proof of the verification theorem is provided, and numerical examples are presented to illustrate some financial implications.

Keywords: Exponential utility; Consumption running maximum; Path-dependent reference; Piecewise feedback control; Verification theorem; 91B16; 91B42; 93E20; 49L12 (search for similar items in EconPapers)
JEL-codes: C61 D11 G11 G41 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)

Downloads: (external link)
http://link.springer.com/10.1007/s00780-022-00475-w Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:finsto:v:26:y:2022:i:2:d:10.1007_s00780-022-00475-w

Ordering information: This journal article can be ordered from
http://www.springer. ... ance/journal/780/PS2

DOI: 10.1007/s00780-022-00475-w

Access Statistics for this article

Finance and Stochastics is currently edited by M. Schweizer

More articles in Finance and Stochastics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().