Diffusive limit approximation of pure-jump optimal stochastic control problems

Marc Abeille (1) , Bruno Bouchard (2) , Lorenzo Croissant (1, 2)

1 Criteo AI Lab
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We consider the diffusive limit of a typical pure-jump Markovian control problem as the intensity of the driving Poisson process tends to infinity. We show that the convergence speed is provided by the Hölder constant of the Hessian of the limit problem, and explain how correction terms can be constructed. This provides an alternative efficient method for the numerical approximation of the optimal control of a pure-jump problem in situations with very high intensity of jump. We illustrate this approach in the context of a display advertising auction problem.

Mots clés: Diffusive limit; stochastic optimal control; online auctions

Domaines: Optimisation et contrôle [math.OC]

Marc Abeille, Bruno Bouchard, Lorenzo Croissant. Diffusive limit approximation of pure-jump optimal stochastic control problems. 2022. ⟨hal-03269700v3⟩