By Stéphane Crépey
Backward stochastic differential equations (BSDEs) offer a common mathematical framework for fixing pricing and threat administration questions of economic derivatives. they're of becoming value for nonlinear pricing difficulties comparable to CVA computations which were constructed because the difficulty. even supposing BSDEs are popular to lecturers, they're much less customary to practitioners within the monetary undefined. with the intention to fill this hole, this publication revisits monetary modeling and computational finance from a BSDE viewpoint, providing a unified view of the pricing and hedging concept throughout all asset periods. It additionally incorporates a evaluation of quantitative finance instruments, together with Fourier suggestions, Monte Carlo equipment, finite variations and version calibration schemes. for you to use in graduate classes in computational finance and monetary modeling, corrected challenge units and Matlab sheets were supplied.
Stéphane Crépey’s book starts off with a couple of chapters on classical stochastic techniques fabric, and then... fasten your seatbelt... the writer begins touring backwards in time via backward stochastic differential equations (BSDEs). this doesn't suggest that one has to learn the e-book backwards, like a manga! fairly, the chance to maneuver backwards in time, no matter if from a number of ultimate eventualities following a likelihood legislation, opens a mess of probabilities for all these pricing difficulties whose resolution isn't really an easy expectation. for instance, this permits for framing difficulties like pricing with credits and investment bills in a rigorous mathematical setup. This is, so far as i do know, the 1st e-book written for numerous degrees of audiences, with purposes to monetary modeling and utilizing BSDEs as one of many major instruments, and because the tune says: "it's by no means nearly as good because the first time".
Damiano Brigo, Chair of Mathematical Finance, Imperial university London
While the classical concept of arbitrage unfastened pricing has matured, and is now good understood and utilized by the finance undefined, the speculation of BSDEs maintains to take pleasure in a fast progress and is still a site constrained to educational researchers and a handful of practitioners. Crépey’s e-book offers this novel method of a much broader group of researchers enthusiastic about mathematical modeling in finance. it's truly an important reference for an individual drawn to the newest advancements in monetary mathematics.
Marek Musiela, Deputy Director of the Oxford-Man Institute of Quantitative Finance
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Extra info for Financial Modeling: A Backward Stochastic Differential Equations Perspective (Springer Finance)
Financial Modeling: A Backward Stochastic Differential Equations Perspective (Springer Finance) by Stéphane Crépey