Convex integral functionals of regular processes

Teemu August Pennanen; Ari-Pekka Perkkio

doi:10.1016/j.spa.2017.08.007

Convex integral functionals of regular processes

Teemu August Pennanen, Ari-Pekka Perkkio

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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 Radon 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.

Original language	English
Pages (from-to)	1652-1677
Journal	Stochastic Processes and Their Applications
Volume	128
Issue number	5
Early online date	24 Aug 2017
DOIs	https://doi.org/10.1016/j.spa.2017.08.007
Publication status	Published - May 2018

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10.1016/j.spa.2017.08.007

Convex integral functionals of_PENNANEN_Publishedonline24August2017_GREEN AAMAccepted author manuscript, 432 KBLicence: CC BY-NC-ND

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AB - This article gives dual representations for convex integral functionalson the linear space of regular processes. This space turns out to be a Banachspace containing many more familiar classes of stochastic processesand its dual can be identified with the space of optional Radon measureswith essentially bounded variation. Combined with classical Banach spacetechniques, 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.

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JO - Stochastic Processes and Their Applications

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Convex integral functionals of regular processes

Abstract

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