عنوان

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

(Number (ISBN

1119166071

(Number (ISBN

111916608X

(Number (ISBN

1119166098

(Number (ISBN

9781119166078

(Number (ISBN

9781119166085

(Number (ISBN

9781119166092

Erroneous ISBN

1119166063

Erroneous ISBN

9781119166061

Title Proper

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

General Material Designation

[Book]

First Statement of Responsibility

Carlos A. Braumann.

Place of Publication, Distribution, etc.

Hoboken, NJ :

Name of Publisher, Distributor, etc.

John Wiley & Sons, Inc.,

Date of Publication, Distribution, etc.

2019.

Date of Publication, Distribution, etc.

©2019

Specific Material Designation and Extent of Item

1 online resource

Text of Note

Includes bibliographical references and index.

Text of Note

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

Text of Note

10.1 Dynkin's formula10.2 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

Text of Note

13 Girsanov's theorem13.1 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

Text of Note

4.3 Some analytical properties4.4 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

Text of Note

7.1 Existence and uniqueness theorem and main proprieties of the solution7.2 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

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Text of Note

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 differential equations and their applications. The author - a noted expert in the field - includes myriad illustrative examples in modelling dynamical phenomena subject to randomness, mainly in biology, bioeconomics and finance, that clearly demonstrate the usefulness of stochastic differential equations in these and many other areas of science and technology. The text also features real-life situations with experimental data, thus covering topics such as Monte Carlo simulation and statistical issues of estimation, model choice and prediction. The book includes the basic theory of option pricing and its effective application using real-life. The important issue of which stochastic calculus, ItO or Stratonovich, should be used in applications is dealt with and the associated controversy resolved. Written to be accessible for both mathematically advanced readers and those with a basic understanding, the text offers a wealth of exercises and examples of application. This important volume: -Contains a complete introduction to the basic issues of stochastic differential equations and their effective application -Includes many examples in modelling, mainly from the biology and finance fields -Shows how to: Translate the physical dynamical phenomenon to mathematical models and back, apply with real data, use the models to study different scenarios and understand the effect of human interventions -Conveys the intuition behind the theoretical concepts -Presents exercises that are designed to enhance understanding -Offers a supporting website that features solutions to exercises and R code for algorithm implementation Written for use by graduate students, from the areas of application or from mathematics and statistics, as well as academics and professionals wishing to study or to apply these models, Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance is the authoritative guide to understanding the issues of stochastic differential equations and their application.

Source for Acquisition/Subscription Address

Safari Books Online

Stock Number

CL0501000067

Title

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

International Standard Book Number

9781119166061

Parallel Title

Stochastic differential equations with applications to modelling in biology and finance

Biology-- Mathematical models.

Finance-- Mathematical models.

Stochastic differential equations.

Biology-- Mathematical models.

Finance-- Mathematical models.

MATHEMATICS-- Applied.

MATHEMATICS-- Probability & Statistics-- General.

Stochastic differential equations.

MAT-- 003000

MAT-- 029000

Number

Edition

Class number

Book number

Braumann, Carlos A.,1951-

Date of Transaction

20200822152607.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y