Elementary Stochastic Calculus, With Finance in View

Abstract

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.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 207 citations exist upstream.