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Some Applications of Linear Programming Formulations in Stochastic Control

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  • Dan Goreac

    (Université Paris-Est)

  • Oana-Silvia Serea

    (Université de Perpignan Via Domitia)

Abstract

We present two applications of the linearization techniques in stochastic optimal control. In the first part, we show how the assumption of stability under concatenation for control processes can be dropped in the study of asymptotic stability domains. Generalizing Zubov’s method, the stability domain is then characterized as some level set of a semicontinuous generalized viscosity solution of the associated Hamilton–Jacobi–Bellman equation. In the second part, we extend our study to unbounded coefficients and apply the method to obtain a linear formulation for control problems whenever the state equation is a stochastic variational inequality.

Suggested Citation

  • Dan Goreac & Oana-Silvia Serea, 2012. "Some Applications of Linear Programming Formulations in Stochastic Control," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 572-593, November.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:2:d:10.1007_s10957-012-0080-z
    DOI: 10.1007/s10957-012-0080-z
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    Cited by:

    1. Li, Jin & Quincampoix, Marc & Renault, Jérôme & Buckdahn, Rainer, 2019. "Representation formulas for limit values of long run stochastic optimal controls," TSE Working Papers 19-1007, Toulouse School of Economics (TSE).

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