2016/03/10 by Getachew K. Befekadu, Befekadu, Getachew K., Alexander Veremyev +3 · 3 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #90C39 #93E20 #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.OC #msc:90C39 #msc:93E20
paper · pdf · doi:10.48550/arxiv.1603.03359
25 Pages - Version 4.0
openalex publication_date 2016/03/10 · arxiv created 2018/01/02 · arxiv updated 2018/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.