The subject of numerical methods in finance has recently emerged as a new discipline at the intersection of probability theory, finance, and numerical analysis. The methods employed bridge the gap between financial theory and computational practice, and provide solutions for complex problems that are difficult to solve by traditional analytical methods. 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 and survey articles focusing on various numerical methods in finance. Key topics covered include: methodological issues, i.e., genetic algorithms, neural networks, Monte-Carlo methods, finite difference methods, stochastic portfolio optimization, as well as the application of other computational and numerical methods in finance and risk management. The book is designed for the academic community and will also serve professional investors. Contributors: K. Amir-Atefi; Z. Atakhanova; A. Biglova; O.J. Blaskowitz; D. D'Souza; W.K. Hรคrdle; I. Huber; I. Khindanova; A. Kohatsu-Higa; P. Kokoszka; M. Montero; S. Ortobelli; E. ร{150}zturkmen; G. Pagรจs; A. Parfionovas; H. Pham; J. Printems; S. Rachev; B. Racheva-Jotova; F. Schlottmann; P. Schmidt; D. Seese; S. Stoyanov; C.E. Testuri; S. Trรผck; S. Uryasev; and Z. Zheng
CONTENT
1 Skewness and Kurtosis Trades -- 2 Valuation of a Credit Spread Put Option: The Stable Paretian model with Copulas -- 3 GARCH-Type Processes in Modeling Energy Prices -- 4 Malliavin Calculus in Finance -- 5 Bootstrap Unit Root Tests for Heavy-Tailed Time Series -- 6 Optimal Portfolio Selection and Risk Management: A Comparison between the Stable Paretian Approach and the Gaussian One -- 7 Optimal Quantization Methods and Applications to Numerical Problems in Finance -- 8 Numerical Methods for Stable Modeling in Financial Risk Management -- 9 Modern Heuristics for Finance Problems: A Survey of Selected Methods and Applications -- 10 On Relation Betweeen Expected Regret and Conditional Value-at-Risk -- 11 Estimation, Adjustment and Application of Transition Matrices in Credit Risk Models -- 12 Numerical Analysis of Stochastic Differential Systems and its Applications in Finance -- List of Contributors
