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2009年度
第６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)
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日時： 2009年12月17日（木）15:00－16:30
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2教室
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Speaker: L. Vostrikova
(Department of Mathematics,
University of Angers, France)
Title: “Minimal f-divergence martingale measures and optimal portfolios for exponential Levy models with a change-point.”
Abstract: The parameters of financial models are generally highly dependent on time. This time-dependency of the parameters can often be described using a piece-wise constant function: we will call this case a change-point problem.Change-point problems have a long history, probably beginning with the papers of Page in an a-posteriori setting, and of Shiryaev in a quickest detection setting. The change-point problem was later considered in many papers, in the context of financial mathematics the question was often related to a quickest detection approach.
Here we study the change-point model for exponential Levy processes when the parameters of the model before and after the change are known and the change-point itself is independent of the observed processes. We obtain the expression for optimal portfolio in a sense of utility maximization.
The problem of utility maximization is highly related with the corresponding f-divergence minimal martingale measure. We find the expression of this f-minimal martingale measure. Then we discuss the problem of conservation of Levy property under this f-minimal martingale measure. Finally, we give f – minimal martingale measures for change-point model and the relatively explicit expression for optimal strategies corresponding to respective utility function.
連絡先：宮原研究室（E-mail: y-miya@econ.nagoya-cu.ac.jp）