Mikosch, T. 　著

内容

目次

Preliminaries - basic concepts from probability theory; stochasticprocesses; Brownian motion; conditional expectation; Martingales; thestochastic integral - the Riemann and Riemann-Stieltjes; integrals; the Itointegral; the Ito lemma; the Stratonovich and other integrals; stochasticdifferential equations - deterministic differential equations; Ito stochasticdifferential equations; the general linear differential equation; numericalsolution; applications of stochastic calculus in finance - the Black-Scholesoption-pricing formula; a useful technique - change of measure. Appendices:modes of convergence; inequalities; non-differentiability and unboundedvariation of Brownian sample paths; proof of the existence of the general Itostochastic integral; the Radon-Nikodym theorem; proof of the existence anduniqueness of the conditional expectation.