We develop a non-anticipative calculus for functionals of a continuous semimartingale, using an extension of the Ito formula to path-dependent functionals which possess certain directional derivatives. The construction is based on a pathwise derivative, introduced by B Dupire, for functionals on the space of right-continuous functions with left limits. We show that this functional derivative ad...

It is shown that a digital simulation of a noise induced phase transition using an algorithm consistent with the Ito stochastic calculus is in agreement with the predictions of that theory, whereas experiments with an analogue simulator yield measured results in agreement with the predictions of the Stratonovich theory.

Diffusions, martingales, and Markov processes are each particular types of stochastic processes. A stochastic process, in a state space E, with parameter set T, is a family (Xt)t∈T of E-valued random variables, or equivalently, a random variable X that takes its values in a space of functions from T to E. Usually, the parameter set T is a subset of R, often [0,∞) or {0, 1, 2, 3, . . .}, the par...

This paper will introduce the Ito’s lemma used in stochastic calculus to obtain Ito-Taylor expansion of a differential equations. The Euler-Maruyama and Milstein’s methods solving equations be discussed derived. We apply these two numerical Black-Scholes model values European call option stock at discretized time intervals. use computer simulation approximate while using formula exact solution....

‎This paper develops iterative method described by [V‎. ‎Daftardar-Gejji‎, ‎H‎. ‎Jafari‎, ‎An iterative method for solving nonlinear functional equations‎, ‎J‎. ‎Math‎. ‎Anal‎. ‎Appl‎. ‎316 (2006) 753-763] to solve Ito stochastic differential equations‎. ‎The convergence of the method for Ito stochastic differential equations is assessed‎. ‎To verify efficiency of method‎, ‎some examples are ex...

Stochastic differential equations and the Black-Scholes PDE. We derived the BlackScholes formula by using arbitrage (risk-neutral) valuation in a discrete-time, binomial tree setting, then passing to a continuum limit. This section explores an alternative, continuoustime approach via the Ito calculus and the Black-Scholes differential equation. This material is very standard; I like Wilmott-How...

We construct a discrete time self-financing portfolio comprised of call options short and stock shares long which is riskless and grows at a fixed rate of return. It is also shown that when shorting periods tend to zero then so devised portfolio turns into the Black-Scholes bond replication. Unlike in standard approach the analysis presented here requires neither Ito Calculus nor solving the He...

This paper presents the design of an ontology to support the assessment process in the technical-scientific subjects (Differential Calculus, Physical, Chemical, among others) which are taught in the firsts years of bachelor’s degree at Instituto Tecnológico de Orizaba (ITO). E-learning is one of the current strategies that facilitates the process of evaluation through the use of Web environment...