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 -