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Optimal impulse control on an unbounded domain with nonlinear cost functions

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  • Stefano Baccarin
  • Simona Sanfelici

Abstract

In this paper we consider the optimal impulse control of a system which evolves randomly in accordance with a homogeneous diffusion process in ℜ 1 . Whenever the system is controlled a cost is incurred which has a fixed component and a component which increases with the magnitude of the control applied. In addition to these controlling costs there are holding or carrying costs which are a positive function of the state of the system. Our objective is to minimize the expected discounted value of all costs over an infinite planning horizon. Under general assumptions on the cost functions we show that the value function is a weak solution of a quasi-variational inequality and we deduce from this solution the existence of an optimal impulse policy. The computation of the value function is performed by means of the Finite Element Method on suitable truncated domains, whose convergence is discussed. Copyright Springer-Verlag Berlin/Heidelberg 2006

Suggested Citation

  • Stefano Baccarin & Simona Sanfelici, 2006. "Optimal impulse control on an unbounded domain with nonlinear cost functions," Computational Management Science, Springer, vol. 3(1), pages 81-100, January.
    • Handle: RePEc:spr:comgts:v:3:y:2006:i:1:p:81-100
    DOI: 10.1007/s10287-005-0045-x
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    Cited by:

    1. Korn, Ralf & Melnyk, Yaroslav & Seifried, Frank Thomas, 2017. "Stochastic impulse control with regime-switching dynamics," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1024-1042.
    2. Ibtissam Hdhiri & Monia Karouf, 2011. "Risk sensitive impulse control of non-Markovian processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(1), pages 1-20, August.
    3. Baccarin, Stefano, 2009. "Optimal impulse control for a multidimensional cash management system with generalized cost functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 198-206, July.

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