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Convex integral functionals of regular processes

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  • Pennanen, Teemu
  • Perkkiö, Ari-Pekka

Abstract

This article gives dual representations for convex integral functionals on the linear space of regular processes. This space turns out to be a Banach space containing many more familiar classes of stochastic processes and its dual can be identified with the space of optional random measures with essentially bounded variation. Combined with classical Banach space techniques, our results allow for a systematic treatment of stochastic optimization problems over BV processes and, in particular, yields a maximum principle for a general class of singular stochastic control problems.

Suggested Citation

  • Pennanen, Teemu & Perkkiö, Ari-Pekka, 2018. "Convex integral functionals of regular processes," Stochastic Processes and their Applications, Elsevier, vol. 128(5), pages 1652-1677.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:5:p:1652-1677
    DOI: 10.1016/j.spa.2017.08.007
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    References listed on IDEAS

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    1. Hiai, Fumio & Umegaki, Hisaharu, 1977. "Integrals, conditional expectations, and martingales of multivalued functions," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 149-182, March.
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    Cited by:

    1. Pennanen, Teemu & Perkkiö, Ari-Pekka, 2023. "Dual spaces of cadlag processes," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 69-93.

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