Nonrecursive Separation of Risk and Time Preferences
28 Pages Posted: 20 Sep 2017
Date Written: October 4, 2016
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: Suggested Citation