Error Calculus for Finance and Physics

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

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

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

"[...] interesting book [...]"
Alexander Schied in: Zentralblatt MATH 12/2007