Optimal smooth consumption and its trade-offs

Philipp Carsten Hornung () and Mogens Steffensen ()
Additional contact information
Philipp Carsten Hornung: University of Copenhagen
Mogens Steffensen: University of Copenhagen

Mathematical Methods of Operations Research, 2025, vol. 102, issue 1, No 2, 29-78

Abstract: Abstract We investigate different ways to design smooth pension products based on solutions to optimal consumption and investment problems. The smoothness of a consumption process can be studied from both a pathwise (measured in terms of quadratic variation) and a pointwise (measured in terms of variance) point of view, and we conclude that introducing one type of smoothing does not necessarily improve the other kind of smoothing. Thus, care must be taken when designing smooth pension products. Focusing on pathwise smoothness without disregarding pointwise smoothness, we provide both a qualitative and a quantitative discussion of the trade-offs involved. In the qualitative discussion, we find that to increase smoothness, it is necessary to reduce the starting value, the drift of consumption, or the level of bequest. For the quantitative discussion, we set up an optimal consumption and investment problem, where the first control is the proportion of wealth invested in the risky asset. Still, the second control is not the consumption process itself. Instead, we use the drift and volatility of consumption as controls. The objective is to minimize the quadratic distance to a target drift and volatility while introducing a penalty for the volatility. We derive explicit solutions to this problem using classic dynamic programming methods and apply them to theoretically and numerically study the three trade-offs. All three approaches result in both pointwise and pathwise smoothing compared to the target, but reducing the drift yields better pointwise smoothing for similar levels of pathwise smoothing.

Keywords: Stochastic control; Quadratic optimization; Consumption-investment problems; Quadratic variation; Pension benefits (search for similar items in EconPapers)
JEL-codes: D11 D15 G11 G22 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00186-025-00902-6 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:mathme:v:102:y:2025:i:1:d:10.1007_s00186-025-00902-6

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/s00186-025-00902-6

Access Statistics for this article

Mathematical Methods of Operations Research is currently edited by Oliver Stein

More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().