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Many mathematical assumptions on which classical derivative pricing methods are based have come under scrutiny in recent years. The present volume offers an introduction to deterministic algorithms for the fast and accurate pricing of derivative contracts in modern finance. This unified, non-Monte-Carlo computational pricing methodology is capable of handling rather general classes of stochastic market models with jumps, including, in particular, all currently used Lévy and stochastic volatility models. It allows us e.g. to quantify model risk in computed prices on plain vanilla, as well as on various types of exotic contracts. The algorithms are developed in classical Black-Scholes markets, and then extended to market models based on multiscale stochastic volatility, to Lévy, additive and certain classes of Feller processes.  The volume is intended for graduate students and researchers, as well as for practitioners in the fields of quantitative finance and applied and computational mathematics with a solid background in mathematics, statistics or economics.

Business mathematics. --- Derivative securities -- Prices -- Mathematical models. --- Finance -- Mathematical models. --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Finance --- Mathematical models. --- Data processing. --- Mathematics. --- Economics, Mathematical. --- Numerical analysis. --- Probabilities. --- Quantitative Finance. --- Numerical Analysis. --- Probability Theory and Stochastic Processes. --- Finance. --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Mathematical analysis --- Funding --- Funds --- Economics --- Currency question --- Economics, Mathematical . --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Mathematical economics --- Econometrics --- Methodology --- Social sciences --- Mathematics in Business, Economics and Finance. --- Probability Theory. --- Derivative securities --- Prices

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This is the first volume of a subseries of the Lecture Notes in Mathematics which will appear randomly over the next years. Each volume will describe some important topic in the theory or applications of Lévy processes and pay tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world. The three expository articles of this first volume have been chosen to reflect the breadth of the area of Lévy processes. The first article by Ken-iti Sato characterizes extensions of the class of selfdecomposable distributions on Rd. The second article by Thomas Duquesne discusses Hausdorff and packing measures of stable trees. The third article by Oleg Reichmann and Christoph Schwab presents numerical solutions to Kolmogoroff equations, which arise for instance in financial engineering, when Lévy or additive processes model the dynamics of the risky assets.

Lévy processes --- Branching processes --- Trees (Graph theory) --- Lévy, Processus de --- Processus ramifiés --- Arbres (Théorie des graphes) --- Lévy processes --- Lévy, Processus de --- Processus ramifiés --- Arbres (Théorie des graphes) --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B