On the hierarchical risk-averse control problems for diffusion processes
Abstract
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 leader and 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 leader as a priority over that of the 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.