A stochastic target problem for branching diffusion processes

Idris Kharroubi and Antonio Ocello

Stochastic Processes and their Applications, 2024, vol. 170, issue C

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.

Keywords: Stochastic target control; Fintech; Cryptocurrencies options; Branching diffusion process; Dynamic programming principle; Hamilton–Jacobi–Bellman equation; Viscosity solution (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2023.104278

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