Convex Integral Functionals of Processes of Bounded Variation

TY - JOUR

T1 - Convex Integral Functionals of Processes of Bounded Variation

AU - Pennanen, Teemu

AU - Perkkio, Ari-Pekka

PY - 2018/2

Y1 - 2018/2

N2 - 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.

AB - 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.

M3 - Article

SN - 0944-6532

VL - 25

SP - 161

EP - 179

JO - JOURNAL OF CONVEX ANALYSIS

JF - JOURNAL OF CONVEX ANALYSIS

IS - 1

ER -