Abstract

This article characterizes conjugates and subdifferentials of convex integral functionals over the linear space of stochastic processes of essentially bounded variation (BV) when the space is identified with the Banach dual of the space of regular processes. Our proofs are based on new results on the interchange of integration and minimization of integral functionals over BV processes. Under mild conditions, the domain of the conjugate is shown to be contained in the space of semimartingales which leads to several applications in the duality theory in stochastic control and mathematical finance.

Author information

Contact details are reproduced from the original publication and may be historical.

Ari-Pekka Perkkiö

Dept. of Mathematics, Ludwig Maximilians Universität, Theresienstr. 39, 80333 München, Germany

perkkioe@math.tu-berlin.de

Keywords

  • Stochastic process
  • bounded variation
  • integral functional
  • convex duality

Mathematics Subject Classification

46N10, 60G07

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Suggested citation

T. Pennanen, A.-P. Perkkiö. “Convex Integral Functionals of Processes of Bounded Variation.” Journal of Convex Analysis 25 (2018), No. 1, 161–179. https://doi.org/10.68381/jca25010

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Published by Heldermann Verlag, 2018. Rights now held by Banach Press.