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Journal of Convex Analysis 25 (2018), No. 1, 161--179
Copyright Heldermann Verlag 2018

Convex Integral Functionals of Processes of Bounded Variation

Teemu Pennanen
Dept. of Mathematics, King's College London, Strand, London WC2R 2LS, England

Ari-Pekka Perkkiö
Dept. of Mathematics, Ludwig Maximilians Universität, Theresienstr. 39, 80333 München, Germany

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.

Keywords: Stochastic process, bounded variation, integral functional, convex duality.

MSC: 46N10, 60G07

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