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A stochastic target problem for branching diffusion processes

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  • Kharroubi, Idris
  • Ocello, Antonio

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. Next, we show that the value function can be simplified into a novel function with the use of a finite-dimensional argument through a concept known as the branching property. Under wide conditions, this last function is shown to be the unique viscosity solution to an HJB variational inequality.

Suggested Citation

  • Kharroubi, Idris & Ocello, Antonio, 2024. "A stochastic target problem for branching diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:spapps:v:170:y:2024:i:c:s0304414923002508
    DOI: 10.1016/j.spa.2023.104278
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