Handbook of Computational and Numerical Methods in Finance

1. Front Matter

   Pages i-ix

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2. Skewness and Kurtosis Trades

   • Oliver J. Blaskowitz, Wolfgang K. Härdle, Peter Schmidt

   Pages 1-14

3. Valuation of a Credit Spread Put Option: The Stable Paretian model with Copulas

   • Dylan D’Souza, Key van Amir-Atefi, Borjana Racheva-Jotova

   Pages 15-69

4. GARCH-Type Processes in Modeling Energy Prices

   • Irina Khindanova, Zauresh Atakhanova, Svetlozar Rachev

   Pages 71-110

5. Malliavin Calculus in Finance

   • Arturo Kohatsu-Higa, Miquel Montero

   Pages 111-174

6. Bootstrap Unit Root Tests for Heavy-Tailed Time Series

   • Piotr Kokoszka, Andrejus Parfionovas

   Pages 175-195

7. Optimal Portfolio Selection and Risk Management: A Comparison between the Stable Paretian Approach and the Gaussian One

   • Sergio Ortobelli, Svetlozar Rachev, Isabella Huber, Almira Biglova

   Pages 197-252

8. Optimal Quantization Methods and Applications to Numerical Problems in Finance

   • Gilles Pagès, Huyên Pham, Jacques Printems

   Pages 253-297

9. Numerical Methods for Stable Modeling in Financial Risk Management

   • Stoyan Stoyanov, Borjana Racheva-Jotova

   Pages 299-329

10. Modern Heuristics for Finance Problems: A Survey of Selected Methods and Applications

    • Frank Schlottmann, Detlef Seese

    Pages 331-359

11. On Relation Betweeen Expected Regret and Conditional Value-at-Risk

    • Carlos E. Testuri, Stanislav Uryasev

    Pages 361-372

12. Estimation, Adjustment and Application of Transition Matrices in Credit Risk Models

    • Stefan Trück, Emrah Özturkmen

    Pages 373-402

13. Numerical Analysis of Stochastic Differential Systems and its Applications in Finance

    • Ziyu Zheng

    Pages 403-429

14. Back Matter

    Pages 431-435

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Numerical Methods in Finance have recently emerged as a new discipline at the intersection of probability theory, finance and numerical analysis. They bridge the gap between financial theory and computational practice and provide solutions to problems where analytical methods are often non-applicable. Numerical methods are more and more used in several topics of financial analy­ sis: computation of complex derivatives; market, credit and operational risk assess­ ment, asset liability management, optimal portfolio theory, financial econometrics and others. Although numerical methods in finance have been studied intensively in recent years, many theoretical and practical financial aspects have yet to be explored. This volume presents current research focusing on various numerical methods in finance. The contributions cover methodological issues. Genetic Algorithms, Neural Net­ works, Monte-Carlo methods, Finite Difference Methods, Stochastic Portfolio Opti­ mization as well as the application of other numerical methods in finance and risk management. As editor, I am grateful to the contributors for their fruitful collaboration. I would particularly like to thankStefan Trueck and Carlo Marinelli for the excellent editorial assistance received over the progress of this project. Thomas Plum did a splendid word-processingjob in preparing the manuscript. lowe much to George Anastassiou (ConsultantEditor, Birkhauser) and Ann Kostant Executive Editor, Mathematics and Physics, Birkhauser for their help and encouragement.

• Probability theory
• algorithms
• calculus
• ksa
• numerical analysis
• optimization
• quantitative finance

"The title of this book my be somewhat misleading-- as an edited volume, it contains several papers on some issues in quantitative finance.  Most contributions have a computational/numerical slant.  It is no surprise that several papers concentrate on heavy-tailed models, in particular Pareto-type models figure prominently. For me, the highlight is the paper by Kohatsu-Higa and Montero on "Malliavan Calculus in Finance". This seventy plus page paper gives a very readable introduction to this imporatnt field of current research.  A further enjoyable paper is "Modern Heuirstics for Finance Problems: A Survey of Selected Mehtods and Applications: by Schlottmann and Seese."

---Publication of the International Statistical Institute

• Department of Statistics and Applied Probability, University of California, Santa Barbara, USA

  Svetlozar T. Rachev

• Department of Economics and Business Engineering, Universität Karlsruhe, Karlsruhe, Germany

  Svetlozar T. Rachev

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