Numerical methods in finance have emerged as a vital field at the crossroads of probability theory, finance and numerical analysis. Based on presentations given at the workshop Numerical Methods in Finance held at the INRIA Bordeaux (France) on June 1-2, 2010, this book provides an overview of the major new advances in the numerical treatment of instruments with American exercises. Naturally it covers the most recent research on the mathematical theory and the practical applications of optimal stopping problems as they relate to financial applications. By extension, it also provides an original treatment of Monte Carlo methods for the recursive computation of conditional expectations and solutions of BSDEs and generalized multiple optimal stopping problems and their applications to the valuation of energy derivatives and assets. The articles were carefully written in a pedagogical style and a reasonably self-contained manner. The book is geared toward quantitative analysts, probabilists, and applied mathematicians interested in financial applications.
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Part I: Particle Methods in Finance.- 1 R. Carmona, P. Del Moral, P. Hu, N, Oudjane: An Introduction to Particle Methods with Financial Applications.- 2.Bhojnarine R. Rambharat: American option valuation with particle filters.- 3.Michael Ludkovski: Monte Carlo Methods for Adaptive Disorder Problems.- Part II: Numerical methods for backward conditional expectations. – 4.Pierre Del Moral, Bruno Rémillard, Sylvain Rubenthale: Monte Carlo approximations of American options that preserve monotonicity and convexity.- 5.Bruno Rémillard, Alexandre Hocquard, Hugues Langlois, and Nicolas Papageorgiou: Optimal Hedging of American Options in Discrete Time.- 6.Gilles Pagès and Benedikt Wilbertz: Optimal Delaunay and Voronoi quantization schemes for pricing American style options.- 7.Bruno Bouchard, Xavier Warin: Monte-Carlo valuation of American options: facts and new algorithms to improve existing methods.- 8.Christian Bender and Jessica Steiner: Least-squares Monte Carlo for backward SDEs.- 9.Lisa J. Powers, Johanna Nešlehová, and David A. Stephens: Pricing American Options in an infinite activity Lévy market: Monte Carlo and deterministic approaches using a diffusion approximation.- 10.Bowen Zhang and Cornelis W. Oosterlee: Fourier Cosine Expansions and Put–Call Relations for Bermudan Options.- Part III: Numerical methods for energy derivatives. – 11.Klaus Wiebauer: A practical view on valuation of multi-exercise American style options in gas and electricity markets.- 12. Marie Bernhart, Huyen Pham, Peter Tankov and Xavier Warin: Swing Options Valuation: a BSDE with Constrained Jumps Approach.- 13.François Turboult and Yassine Youlal: Swing option pricing by optimal exercise boundary estimation.- 14.Xavier Warin: Gas Storage Hedging.- 15.J.Frédéric Bonnans, Zhihao Cen, Thibault Christel: Sensitivity analysis of energy contractsby stochastic programming techniques.
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