  In this paper, we consider a risk-averse decision problem for
controlled-diffusion processes, with dynamic risk measures, in which multiple
risk-averse agents choose their decisions in such a way to minimize their
individual accumulated risk-costs over a finite-time horizon. In particular, we
introduce multi-structure dynamic risk measures induced from conditional
$g$-expectations, where the latter are associated with the generator
functionals of certain BSDEs that implicitly take into account the risk-cost
functionals of the risk-averse agents. Here, we also require that such
solutions of the BSDEs to satisfy a stochastic viability property with respect
to a given closed convex set. Moreover, using a result similar to that of the
Arrow-Barankin-Blackwell theorem, we establish the existence of consistent
optimal decisions for the risk-averse agents, when the set of all Pareto
optimal solutions, in the sense of viscosity, for the associated dynamic
programming equations is dense in the given closed convex set. Finally, we
briefly comment on the characteristics of acceptable risks vis-\'{a}-vis some
uncertain future costs or outcomes, in which results from the dynamic risk
analysis constitute part of the information used in the risk-averse decision
criteria.
