Diffusive Limit Approximation of Pure-Jump Optimal Stochastic Control Problems

Marc Abeille (), Bruno Bouchard () and Lorenzo Croissant ()
Additional contact information
Marc Abeille: Criteo AI Lab.
Bruno Bouchard: Université Paris-Dauphine, PSL, CNRS
Lorenzo Croissant: Criteo AI Lab.

Journal of Optimization Theory and Applications, 2023, vol. 196, issue 1, No 7, 147-176

Abstract: Abstract 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 exponent 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 jumps. We illustrate this approach in the context of a display advertising auction problem.

Keywords: Diffusive limit; Stochastic optimal control; Online auctions (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-022-02135-7

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