2007年度 第４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 )
講師： Michael Kupper(ETH)
タイトル： On Divergence Utilities and the Composition of Time-Consistent Dynamic Monetary Risk Measures in Discrete Time
Abstract: We investigate a class of concave monetary utility functions, which we call divergence utilities. Divergence utilities can be viewed as the translation invariant hull of classical expected utilities. This class is rather wide and includes, in particular, the entropic utility. More important, this class is very convenient analytically. We provide several representations of the corresponding concave utilities, an explicit solution of the portfolio optimization problem as well as an explicit solution of the risk sharing problem.
In the second part of the talk, we discuss dynamic risk measures (the negative of a monetary utility function). In discrete time, every time-consistent dynamic monetary risk measure can be written as a composition of one-step risk measures. We exploit this structure to give new dual representation results for time-consistent convex monetary risk measures in terms of one-step penalty functions. We study risk measures for random variables modeling financial positions at a fixed future time. Then we consider the more general case of risk measures that depend on stochastic processes describing the evolution of financial positions or cumulated cash flows. In both cases the new representations allow for a simple composition of one-step risk measures in the dual. We discuss several explicit examples.
(The talk is based on joint works with Alexander Cherny and Patrick Cheridito.)
日時： ２００７年９月５日（水）午後３：００－５：００
場所： 名古屋市立大学経済学部棟１階大学院第３教室（予定）
―――――――――――――――――――――――――――――
（世話人：宮原孝夫 Tel:052-872-5718 
）