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Titre	Option Theory with Stochastic Analysis: An Introduction to Mathematical Finance (Universitext) (English Edition)
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Option Theory with Stochastic Analysis: An Introduction to Mathematical Finance (Universitext) (English Edition)

Catégorie: Loisirs créatifs, décoration et passions, Religions et Spiritualités, Art, Musique et Cinéma
Auteur: Michelle Obama
Éditeur: Alessandra Hazard
Publié: 2017-06-24
Écrivain: Callie Hart, Walter Murch
Langue: Tagalog, Persan, Grec ancien, Roumain, Catalan
Format: Livre audio, pdf

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The Black-Scholes option pricing problem in mathematical finance: generalization and extensions for a large class of stochastic processes - The ability to price risks and devise optimal investment strategies in thé présence of an uncertain "random" market is thé cornerstone of modern finance theory. We first consider thé simplest such problem of a so-called "European call option" initially solved by Black and Scholes using Ito stochastic calculus for markets modelled by a log-Brownien stochastic process. A simple and powerful formalism is presented which allows us to generalize thé analysis to a large class of stochastic processes, such as ARCH, jump or Lévy processes. We also address thé case of correlated Gaussian processes, which is shown to be a good description of three différent market indices (MATIF, CAC40, FTSE100). Our main result is thé introduction of thé concept of an optimal strategy in the sense of (functional) minimization of the risk with respect to the portfolio. If the risk may be made to vanish for particular continuous uncorrelated 'quasiGaussian' stochastic processes (including Black and Scholes model), this is no l

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