A Stochastic Target Problem for Branching Diffusions
Abstract
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.
Keywords
Cite
@article{arxiv.2206.13267,
title = {A Stochastic Target Problem for Branching Diffusions},
author = {Idris Kharroubi and Antonio Ocello},
journal= {arXiv preprint arXiv:2206.13267},
year = {2022}
}