2016/10/23 by Getachew K. Befekadu, Befekadu, Getachew K., Eduardo L. Pasiliao +1 · 2 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.OC
paper · pdf · doi:10.48550/arxiv.1610.07201
26 Pages. (Additional Note: This work is, in some sense, a continuation of our previous paper arXiv:1603.03359.)
arxiv created 2016/10/23 · openalex publication_date 2016/10/23 · arxiv updated 2016/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider a risk-averse decision problem for controlled-diffusion processes, with dynamic risk measures, in which there are two risk-averse decision makers (i.e., \it leader and \it follower) with different risk-averse related responsibilities and information. Moreover, we assume that there are two objectives that these decision makers are expected to achieve. That is, the first objective being of \it stochastic controllability type that describes an acceptable risk-exposure set vis-á-vis some uncertain future payoff, and while the \it second one is making sure the solution of a certain risk-related system equation has to stay always above a given continuous stochastic process, namely \it obstacle. In particular, we introduce multi-structure, time-consistent, dynamic risk measures induced from conditional g-expectations, where the latter are associated with the generator functionals of two backward-SDEs that implicitly take into account the above two objectives along with the given continuous obstacle process. Moreover, under certain conditions, we establish the existence of optimal hierarchical risk-averse solutions, in the sense of viscosity solutions, to the associated risk-averse dynamic programming equations that formalize the way in which both the \it leader and \it follower consistently choose their respective risk-averse decisions. Finally, we remark on the implication of our result in assessing the influence of the \it leader's decisions on the risk-averseness of the \it follower in relation to the direction of \it leader-follower information flow.