TY - JOUR

T1 - Nonrecursive separation of risk and time preferences

AU - Fahrenwaldt, Matthias Albrecht

AU - Jensen, Ninna Reitzel

AU - Steffensen, Mogens

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Certainty equivalents

KW - Equilibrium strategies

KW - Generalized Hamilton–Jacobi–Bellman equation

KW - Recursive utility

KW - Time-consistency

KW - Time-global preferences

UR - http://www.scopus.com/inward/record.url?scp=85088217461&partnerID=8YFLogxK

U2 - 10.1016/j.jmateco.2020.07.002

DO - 10.1016/j.jmateco.2020.07.002

M3 - Journal article

AN - SCOPUS:85088217461

VL - 90

SP - 95

EP - 108

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

SN - 0304-4068

ER -