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 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, Itô 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.

CARLOS A. BRAUMANN is Professor in the Department of Mathematics and member of the Research Centre in Mathematics and Applications, Universidade de Évora, Portugal. He is an elected member of the International Statistical Institute (since 1992), a former President of the European Society for Mathematical and Theoretical Biology (2009-12) and of the Portuguese Statistical Society (2006-09 and 2009-12), and a former member of the European Regional Committee of the Bernoulli Society (2008-12). He has dealt with stochastic differential equation (SDE) models and applications (mainly biological).