Nonrecursive Separation of Risk and Time Preferences

28 Pages Posted: 20 Sep 2017

See all articles by Matthias Fahrenwaldt

Matthias Fahrenwaldt

Heriot-Watt University - Department of Actuarial Mathematics and Statistics

Ninna Jensen

University of Copenhagen

Mogens Steffensen

University of Copenhagen

Date Written: October 4, 2016

Abstract

Recursive utility disentangles preferences with respect to time and risk by recursively building up a value function of local increments. This involves certainty equivalents of indirect utility. Instead we disentangle preferences with respect to time and risk by building up a value function as a non-linear aggregation of certainty equivalents of direct utility of consumption. This entails time-consistency issues which are dealt with by looking for an equilibrium control and an equilibrium value function rather than a classical optimal control and a classical optimal value function. We characterize the solution in a general diffusive incomplete market model and find that, in certain special cases of utmost interest, the characterization coincides with what would arise from a recursive utility approach. But also importantly, in other cases, it does not: The two approaches are fundamentally different but match, exclusively but importantly, in the mathematically special case of homogeneity of the value function.

Keywords: time-consistency, time-global preferences, recursive utility, equilibrium strategies, generalized Hamilton–Jacobi–Bellman equation, continuous time, certainty equivalents

JEL Classification: C61, G11

Suggested Citation

Fahrenwaldt, Matthias and Jensen, Ninna and Steffensen, Mogens, Nonrecursive Separation of Risk and Time Preferences (October 4, 2016). Available at SSRN: https://ssrn.com/abstract=3039095 or http://dx.doi.org/10.2139/ssrn.3039095

Matthias Fahrenwaldt

Heriot-Watt University - Department of Actuarial Mathematics and Statistics ( email )

Edinburgh, Scotland EH14 4AS
United Kingdom

Ninna Jensen

University of Copenhagen ( email )

Universitetsparken 5
Copenhagen, DK-2100
Denmark

Mogens Steffensen (Contact Author)

University of Copenhagen ( email )

Universitetsparken 5
DK-2100 Copenhagen
Denmark

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