Ergodic control of diffusions with compound Poisson jumps under a general structural hypothesis |
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Institution: | 1. Faculty of Economics and Business Administration, Goethe University, Frankfurt am Main, Germany;2. Department IV – Mathematics, University of Trier, Trier, Germany |
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Abstract: | We study the ergodic control problem for a class of controlled jump diffusions driven by a compound Poisson process. This extends the results of Arapostathis et al. (2019) to running costs that are not near-monotone. This generality is needed in applications such as optimal scheduling of large-scale parallel server networks.We provide a full characterizations of optimality via the Hamilton–Jacobi–Bellman (HJB) equation, for which we additionally exhibit regularity of solutions under mild hypotheses. In addition, we show that optimal stationary Markov controls are a.s. pathwise optimal. Lastly, we show that one can fix a stable control outside a compact set and obtain near-optimal solutions by solving the HJB on a sufficiently large bounded domain. This is useful for constructing asymptotically optimal scheduling policies for multiclass parallel server networks. |
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Keywords: | Controlled jump diffusions ergodic Hamilton–Jacobi–Bellman (HJB) equation Stable Markov optimal control Pathwise optimality Approximate HJB equation Spatial truncation |
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