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Impulse and Continuous Stochastic Control: A Dynamic Programming Approach

  • Alexander A. Yushkevich
Conference paper

Abstract

1. A predominant approach to impulse stochastic control is that by functional analysis methods (Bensoussan et Lions (1982)). It originated as a generalization of optimal stopping and an appropriate field of applications of quasivaraitional inequalities (=QVI). One understands here impulse actions as deterministic shifts of the state made at sequentially increasing stopping times, usually without a continuous control between them. As to instantaneous iterations of impulse actions, in most works they are excluded either by definition or informally by a cost structure which makes such iterations certainly unprofitable; in others they are ignored while formally not forbidden. Started with diffusion processes, the study was extended later to other cases, among them to piecewise-deterministic processes (=PDP; Costa and Davis (1989)).

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References

  1. Bensoussan A, Lions J.L (1982) Contrôle impulsionnel et inéquations quasi variationnelles. Dunod. ParisGoogle Scholar
  2. Costa O.L.V., Davis M.H.A (1989) Impulse control of piecewise-deterministic processes. Math Control Signal Systems 1:187–208CrossRefGoogle Scholar
  3. Donchev D.S (1990) The two-armed bandit problem with continuous time in the presence of gradual and impulsive controls. Russian Math Surveys 451:200–202CrossRefGoogle Scholar
  4. van der Duyn Schouten F.A. (1983) Markov decision processes with continuous time parameter. Math Centrum Tracts. AmsterdamGoogle Scholar
  5. Yushkevich A.A (1989) Verification theorems for Markov decision processes with controlled deterministic drift and gradual and impulsive controls. Theory Prob 34:474–496CrossRefGoogle Scholar
  6. Yushkevich A.A (1992) On a two-armed bandit problem with impulse controls and discounting. Russian Math Surveys (submitted)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Alexander A. Yushkevich
    • 1
  1. 1.Department of MathematicsUniverstiy of North Carolina at CharlotteCharlotteUSA

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