  We consider an optimal stochastic target problem for branching diffusion
processes. This problem consists in finding the minimal condition for which a
control allows the underlying branching process to reach a target set at a
finite terminal time for each of its branches. This problem is motivated by an
example from fintech where we look for the super-replication price of options
on blockchain based cryptocurrencies. We first state a dynamic programming
principle for the value function of the stochastic target problem. We then show
that the value function can be reduced to a new function with a finite
dimensional argument by a so called branching property. Under wide conditions,
this last function is shown to be the unique viscosity solution to an HJB
variational inequality.
