Introduction to stochastic differential equations with applications to modelling in biology and finance

Introduction to stochastic differential equations with applications to modelling in biology and finance

A comprehensive introduction to the core issues of stochastic differential equations and their effective application Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance offers a comprehensive examination to the most important issues of stochastic d...

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Detalles Bibliográficos
Otros Autores: Braumann, Carlos A., 1951- author (author)
Formato: Libro electrónico
Idioma:Inglés
Publicado: Hoboken, NJ ; West Sussex, UK : Wiley 2019.
Edición:1st edition
Materias:
Stochastic differential equations.
Biology > Mathematical models.
Finance > Mathematical models.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009631481506719
Tabla de Contenidos:
  • Intro
  • Table of Contents
  • Preface
  • About the companion website
  • 1 Introduction
  • 2 Revision of probability and stochastic processes
  • 2.1 Revision of probabilistic concepts
  • 2.2 Monte Carlo simulation of random variables
  • 2.3 Conditional expectations, conditional probabilities, and independence
  • 2.4 A brief review of stochastic processes
  • 2.5 A brief review of stationary processes
  • 2.6 Filtrations, martingales, and Markov times
  • 2.7 Markov processes
  • 3 An informal introduction to stochastic differential equations
  • 4 The Wiener process
  • 4.1 Definition
  • 4.2 Main properties
  • 4.3 Some analytical properties
  • 4.4 First passage times
  • 4.5 Multidimensional Wiener processes
  • 5 Diffusion processes
  • 5.1 Definition
  • 5.2 Kolmogorov equations
  • 5.3 Multidimensional case
  • 6 Stochastic integrals
  • 6.1 Informal definition of the Itô and Stratonovich integrals
  • 6.2 Construction of the Itô integral
  • 6.3 Study of the integral as a function of the upper limit of integration
  • 6.4 Extension of the Itô integral
  • 6.5 Itô theorem and Itô formula
  • 6.6 The calculi of Itô and Stratonovich
  • 6.7 The multidimensional integral
  • 7 Stochastic differential equations
  • 7.1 Existence and uniqueness theorem and main proprieties of the solution
  • 7.2 Proof of the existence and uniqueness theorem
  • 7.3 Observations and extensions to the existence and uniqueness theorem
  • 8 Study of geometric Brownian motion (the stochastic Malthusian model or Black-Scholes model)
  • 8.1 Study using Itô calculus
  • 8.2 Study using Stratonovich calculus
  • 9 The issue of the Itô and Stratonovich calculi
  • 9.1 Controversy
  • 9.2 Resolution of the controversy for the particular model
  • 9.3 Resolution of the controversy for general autonomous models
  • 10 Study of some functionals
  • 10.1 Dynkin's formula
  • 10.2 Feynman-Kac formula.
  • 11 Introduction to the study of unidimensional Itô diffusions
  • 11.1 The Ornstein-Uhlenbeck process and the Vasicek model
  • 11.2 First exit time from an interval
  • 11.3 Boundary behaviour of Itô diffusions, stationary densities, and first passage times
  • 12 Some biological and financial applications
  • 12.1 The Vasicek model and some applications
  • 12.2 Monte Carlo simulation, estimation and prediction issues
  • 12.3 Some applications in population dynamics
  • 12.4 Some applications in fisheries
  • 12.5 An application in human mortality rates
  • 13 Girsanov's theorem
  • 13.1 Introduction through an example
  • 13.2 Girsanov's theorem
  • 14 Options and the Black-Scholes formula
  • 14.1 Introduction
  • 14.2 The Black-Scholes formula and hedging strategy
  • 14.3 A numerical example and the Greeks
  • 14.4 The Black-Scholes formula via Girsanov's theorem
  • 14.5 Binomial model
  • 14.6 European put options
  • 14.7 American options
  • 14.8 Other models
  • 15 Synthesis
  • References
  • Index
  • End User License Agreement.

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