  In intertemporal settings, the multiattribute utility theory of Kihlstrom and
Mirman suggests the application of a concave transform of the lifetime utility
index. This construction, while allowing time and risk attitudes to be
separated, leads to dynamically inconsistent preferences. We address this issue
in a game-theoretic sense by formalizing an equilibrium control theory for
continuous-time Markov processes. In these terms, we describe the equilibrium
strategy and value function as the solution of an extended
Hamilton-Jacobi-Bellman system of partial differential equations. We verify
that (the solution of) this system is a sufficient condition for an equilibrium
and examine some of its novel features. A consumption-investment problem for an
agent with CRRA-CES utility showcases our approach.
