分野別セミナー

アブストラクト:
This talk is concerned with a class of convex
　functionals on $L^¥infty$ defined as sublinear
　expectations of random convex functions. This
　class is viewed as a robust version of the
　classical notion of convex integral functionals,
　for which the complete description of their
　conjugates had been obtained by R. T. Rockafellar.
　The first aim of this talk is to prove a
　``Rockafellar-type'' theorem for our robust

　convex functionals, giving the description of
　conjugates.　The original motivation of this study was to
　give an elegant proof of a duality in an optimal
　investment problem in finance, which is the
　content of the second half of the talk. Namely,
　we shall prove, by our Rockafellar-type theorem,
　the duality between a robust utility maximization
　problem and a minimization of a certain
　(generalized) entropic functional over a class
　of local martingale measures. Finally, we conclude
with some explicit examples by means of quadratic
BSDE's.

　This talk is based on the preprint:
　Duality in robust utility maximization with
　unbounded claim via a robust extension of
　Rockafellar's theorem, arXiv:1101.2968.