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Diffusive limit approximation of pure jump optimal ergodic control problems

Abeille, Marc; Bouchard, Bruno; Croissant, Lorenzo (2022), Diffusive limit approximation of pure jump optimal ergodic control problems, Journal of Optimization Theory and Applications, p. 42. 10.1007/s10957-022-02135-7

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Type
Article accepté pour publication ou publié
Date
2022
Journal name
Journal of Optimization Theory and Applications
Publisher
Springer
Published in
Paris
Pages
42
Publication identifier
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Author(s)
Abeille, Marc
Bouchard, Bruno
Croissant, Lorenzo
Abstract (EN)
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.
Subjects / Keywords
Diffusive limit; Stochastic optimal control; Online auctions