A Stochastic Target Problem for Branching Diffusions - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2022

A Stochastic Target Problem for Branching Diffusions

Résumé

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.
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Dates et versions

hal-03695036 , version 1 (14-06-2022)
hal-03695036 , version 2 (16-06-2022)
hal-03695036 , version 3 (23-06-2022)

Identifiants

  • HAL Id : hal-03695036 , version 1

Citer

Idris Kharroubi, Antonio Ocello. A Stochastic Target Problem for Branching Diffusions. 2022. ⟨hal-03695036v1⟩
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