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 Elementary Stochastic Calculus, with Finance in View by Mikosch, Thomas |
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Brief Description An elementary introduction to modelling with Ito integral or stochastic differential equations, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black-Scholes option pricing formula is derived. |
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Synopsis Modelling with the Ito integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory. This text should be suitable for the reader without a deep mathematical background. It seeks to provide an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black-Scholes option pricing formula is derived. |
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Table of Contents Preliminaries basic concepts from probability theory; stochastic processes; Brownian motion; conditional expectation; Martingales; the stochastic integral the Riemann and Riemann-Stieltjes; integrals; the Ito integral; the Ito lemma; the Stratonovich and other integrals; stochastic differential equations deterministic differential equations; Ito stochastic differential equations; the general linear differential equation; numerical solution; applications of stochastic calculus in finance the Black-Scholes option-pricing formula; a useful technique change of measure. Appendices: modes of convergence; inequalities; non-differentiability and unbounded variation of Brownian sample paths; proof of the existence of the general Ito stochastic integral; the Radon-Nikodym theorem; proof of the existence and uniqueness of the conditional expectation. |
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Related Links - Countrybookshop Bestselling Authors in Stochastics Lamberton, D.McLean Rogers, L.C.G. Allen, Linda J.S. Jones, P.W. Mikosch, Thomas Soderstrom, Torsten |
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