Bellman equations for scalar linear convex stochastic control problems

Volume 122 / 2020

Tyrone Duncan, Bozenna Pasik Duncan, Łukasz Stettner Banach Center Publications 122 (2020), 77-92 MSC: Primary: 93E20; Secondary: 60J20, 93E24. DOI: 10.4064/bc122-5

Abstract

A family of discrete time stochastic control problems with linear dynamics and convex cost functionals are studied. For the case of a scalar control for such a model with additive finite time horizon, discounted, and average cost per unit time convex cost functionals as well as multiplicative (exponential) finite time horizon, discounted and long run average convex functionals explicit solutions are described for suitable Bellman equations. In the particular case of a linear quadratic control problem a general continuous time problem is described. The form of the optimal strategies for each of these control problems is characterized.

Authors

  • Tyrone DuncanDepartment of Mathematics
    University of Kansas
    Lawrence, KS 66045
    e-mail
  • Bozenna Pasik DuncanDepartment of Mathematics
    University of Kansas
    Lawrence, KS 66045
    e-mail
  • Łukasz StettnerInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-656 Warszawa, Poland
    e-mail

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