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Convex Integral Functionals of Processes of Bounded Variation

Research output: Contribution to journalArticle

Teemu Pennanen, Ari-Pekka Perkkio

Original languageEnglish
Pages (from-to)161-179
JournalJOURNAL OF CONVEX ANALYSIS
Volume25
Issue number1
Early online date31 Jan 2017
Accepted/In press16 Jan 2017
E-pub ahead of print31 Jan 2017
PublishedFeb 2018

King's Authors

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.

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