  In this paper, we consider a risk-averse control problem for diffusion
processes, in which there is a partition of the admissible control strategy
into two decision-making groups (namely, the {\it leader} and {\it follower})
with different cost functionals and risk-averse satisfactions. Our approach,
based on a hierarchical optimization framework, requires that a certain level
of risk-averse satisfaction be achieved for the {\it leader} as a priority over
that of the {\it follower's} risk-averseness. In particular, we formulate such
a risk-averse control problem involving a family of time-consistent dynamic
convex risk measures induced by conditional $g$-expectations (i.e.,
filtration-consistent nonlinear expectations associated with the generators of
certain backward stochastic differential equations). Moreover, under suitable
conditions, we establish the existence of optimal risk-averse solutions, in the
sense of viscosity solutions, for the corresponding risk-averse dynamic
programming equations. Finally, we briefly comment on the implication of our
results.
