Error Calculus for Finance and Physics: The Language of Dirichlet Forms

ISBN-13: 9783110180367 / Angielski / Twarda / 2003 / 244 str.

Nicolas Bouleau

Opis

The book deals with propagation of errors on data through mathematical models with applications in finance and physics. It is interesting for scientists and practitioners when studying the sensitivity of their models to small changes in the hypotheses. The book differs from what is usually done in sensitivity analysis because it yields powerful new tools allowing to manage errors in stochastic models as those used in modern finance.

Recenzje

"(...) interesting book (...)" (Alexander Schied in: Zentralblatt MATH 12/2007)

Spis treści

Intuitive introduction to error structures · Error magnitude · Description of small errors by their biases and variances · Intuitive notion of error structure · How to proceed with an error calculation · Application: Partial integration for a Markov chain · Appendix. Historical comment: The benefit of randomizing physical or natural quantities · Bibliography for Chapter I

Strongly-continuous semigroups and Dirichlet forms · Strongly-continuous contraction semigroups on a Banach space · The Ornstein-Uhlenbeck semigroup on R and the associated Dirichlet form · Appendix. Determination of D for the Ornstein-Uhlenbeck semigroup · Bibliography for Chapter II

Error structures · Main definition and initial examples · Performing calculations in error structures · Lipschitz functional calculus and existence of densities · Closability of pre-structures and other examples · Bibliography for Chapter III

Images and products of error structures · Images · Finite products · Infinite products · Appendix. Comments on projective limits · Bibliography for Chapter IV

Sensitivity analysis and error calculus · Simple examples and comments · The gradient and the sharp · Integration by parts formulae · Sensitivity of the solution of an ODE to a functional coefficient · Substructures and projections · Bibliography for Chapter V

Error structures on fundamental spaces · Error structures on the Monte Carlo space · Error structures on the Wiener space · Error structures on the Poisson space · Bibliography for Chapter VI

Application to financial models · Instantaneous error structure of a financial asset · From an instantaneous error structure to a pricing model · Error calculations on the Black-Scholes model · Error calculations for a diffusion model · Bibliography for Chapter VII

Applications in the field of physics · Drawing an ellipse (exercise) · Repeated samples: Discussion · Calculation of lengths using the Cauchy-Favard method (exercise) · Temperature equilibrium of a homogeneous solid (exercise) · Nonlinear oscillator subject to thermal interaction: The Grüneisen parameter · Natural error structures on dynamic systems · Bibliography for Chapter VIII

O autorze

Nicolas Bouleau is Scientific Director at the École Nationale des Ponts, Champs-sur-Marne, France.