Geodesic
Convex Integral Functionals of Processes of Bounded Variation
Journal of convex analysis, Tome 25 (2018) no. 1, pp. 161-179
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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.
Classification : 46N10, 60G07
Mots-clés : Stochastic process, bounded variation, integral functional, convex duality 
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     author = {T. Pennanen and A.-P. Perkki\"o},
     title = {Convex {Integral} {Functionals} of {Processes} of {Bounded} {Variation}},
     journal = {Journal of convex analysis},
     pages = {161--179},
     year = {2018},
     volume = {25},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2018_25_1_JCA_2018_25_1_a9/}
}
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T. Pennanen; A.-P. Perkkiö. Convex Integral Functionals of Processes of Bounded Variation. Journal of convex analysis, Tome 25 (2018) no. 1, pp. 161-179. http://geodesic.mathdoc.fr/item/JCA_2018_25_1_JCA_2018_25_1_a9/