Evolution of the Arrow–Pratt measure of risk-tolerance for predictable forward utility processes

Moris S. Strub () and Xun Yu Zhou ()
Additional contact information
Moris S. Strub: Southern University of Science and Technology
Xun Yu Zhou: Columbia University

Finance and Stochastics, 2021, vol. 25, issue 2, No 5, 358 pages

Abstract: Abstract We study the evolution of the Arrow–Pratt measure of risk-tolerance in the framework of discrete-time predictable forward utility processes in a complete semimartingale financial market. An agent starts with an initial utility function, which is then sequentially updated forward at discrete times under the guidance of a martingale optimality principle. We mostly consider a one-period framework and first show that solving the associated inverse investment problem is equivalent to solving some generalised integral equations for the inverse marginal function or for the conjugate function, both associated with the forward utility. We then completely characterise the class of forward utility pairs that can have a time-invariant measure of risk-tolerance and thus a preservation of preferences in time. Next, we show that in general, preferences vary over time and that whether the agent becomes more or less tolerant to risk is related to the curvature of the measure of risk-tolerance of the forward utility pair. Finally, to illustrate the obtained general results, we present an example in a binomial market model where the initial utility function belongs to the SAHARA class, and we find that this class is analytically tractable and stable in the sense that all the subsequent utility functions belong to the same class as the initial one.

Keywords: Risk-aversion; Portfolio selection; Semimartingale model; Forward utility processes; Dynamic preferences; Complete financial market; Binomial model; SAHARA utility; 91B06; 91B16; 91G10; 45A05 (search for similar items in EconPapers)
JEL-codes: C60 D81 G11 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s00780-020-00444-1 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:25:y:2021:i:2:d:10.1007_s00780-020-00444-1

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

DOI: 10.1007/s00780-020-00444-1

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 ().