2009年度
第7回「数理ファイナンスセミナー」
(名古屋市立大学経済学研究科 宮原研究室)
日時：2010年2月8日（月）13:30－15:00
会場：名古屋市立大学山の畑キャンパス
3号館（経済学部棟）1階大学院第1教室
講演者: 尾張 圭太（一橋大学・経済学研究科）
タイトル: On Convex Duality Methods for Subjective and Robust Utility
Maximization with Unbounded Random Endowment.
概要: We address the applicability of the convex duality method for utility maximization, in the presence of random endowment. When the price process is a locally bounded semimartingale, we show that the fundamental duality relation holds true, for a wide class of utility functions and unbounded random endowments. We show this duality by exploiting Rockafellar’s theorem on integral functional (Pacific J. Math. 39, 439-469, 1971), to a random utility function, which allows us to apply Fenchel’s duality theorem.
Furthermore, we shall extend the duality to the framework of robust utility maximization which is the maximization of point-wise infimum of $P$-expected utility functionals when $P$-runs through a convex set of probabilities. One (standard) way of doing so is to reduce the “robust” problem to a family of “subjective” problems with the help of minimax theorem. This approach, however, requires an additional technical assumption on the utility function, thus we do not employ. Instead, we extend Rockafellar’s fundamental theorem on convex integral functional to the point-wise supremum of such functionals, giving a description of conjugate functional under sufficiently general (at least for utility maximization) assumptions. Then the duality follows from Fenchel’s general duality theorem as the subjective case.
———————————–
連絡先：宮原研究室（E-mail y-miya(at)econ.nagoya-cu.ac.jp）