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Product Details
- Hardcover: 266 pages
- Publisher: Springer; 1 edition (October 1, 2009)
- Language: English
- ISBN-10: 3642026079
- ISBN-13: 978-3642026072
Editorial ReviewsProduct Description
Problems of stochastic optimization and various mathematical aspects of risk are the main themes of this contributed volume. The readers learn about the recent results and techniques of optimal investment, risk measures and derivative pricing. There are also papers touching upon credit risk, martingale theory and limit theorems.
Forefront researchers in probability and financial mathematics have contributed to this volume paying tribute to Yuri Kabanov, an eminent researcher in probability and mathematical finance, on the occasion of his 60th birthday. The volume gives a fair overview of these topics and the current approaches.
CONTENT
On the Extension of the Namioka-Klee Theorem and on the Fatou
Property for Risk Measures . . . . . . . . . . . . . . . . . . . . . . . 1
Sara Biagini and Marco Frittelli
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 The Extended Namioka Theorem . . . . . . . . . . . . . . . . . . 7
2.1 TheCurrentLiterature . . . . . . . . . . . . . . . . . . . . 9
3 On Order Lower Semicontinuity in Riesz Spaces . . . . . . . . . . 10
3.1 EquivalentFormulationsofOrder l.s.c. . . . . . . . . . . . 11
3.2 The Order Continuous Dual 1∼
n . . . . . . . . . . . . . . . 12
4 On the C-Property . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.1 The C-Property in the Representation of Convex and
Monotone Functionals . . . . . . . . . . . . . . . . . . . . 14
5 Orlicz Spaces and Applications to Risk Measures . . . . . . . . . 16
5.1 Orlicz Spaces Have the C-Property . . . . . . . . . . . . . 16
5.2 New Insights on the Downside Risk and Risk Measures
Associated to a Utility Function u . . . . . . . . . . . . . . 19
5.3 Quadratic-Flat Utility . . . . . . . . . . . . . . . . . . . . 26
5.4 Exponential Utility . . . . . . . . . . . . . . . . . . . . . . 27
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
On Certain Distributions Associated with the Range of Martingales . . . 29
Alexander Cherny and Bruno Dupire
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Differentiability Properties of Utility Functions . . . . . . . . . . . . . . . 39
Freddy Delbaen
1 NotationandPreliminaries . . . . . . . . . . . . . . . . . . . . . 39
2 The Jouini-Schachermayer-Touzi Theorem . . . . . . . . . . . . . 42
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