The goal of this book is to develop robust, accurate and efficient numerical methods to price a
number of derivative products in quantitative finance.We focus on one-factor and multi-factor
models for a wide range of derivative products such as options, fixed income products, interest
rate products and ‘real’ options. Due to the complexity of these products it is very difficult to
find exact or closed solutions for the pricing functions. Even if a closed solution can be found
it may be very difficult to compute. For this and other reasons we need to resort to approximate
Computational fluid dynamics (CFD) is concerned with the efficient numerical solution of the partial differential equations that describe fluid dynamics. CFD techniques are commonly used in the many areas of engineering where fluid behavior is an important factor. Traditional fields of application include aerospace and automotive design, and more recently, bioengineering and consumer and medical electronics.
This book presents and develops major numerical methods currently used for solving
problems arising in quantitative finance. Our presentation splits into two parts.
Part I is methodological, and offers a comprehensive toolkit on numerical methods
and algorithms. This includes Monte Carlo simulation, numerical schemes for
partial differential equations, stochastic optimization in discrete time, copula functions,
transform-based methods and quadrature techniques.
Part II is practical, and features a number of self-contained cases.
This section attempts to answer some of the questions you might formulate when you turn the first page: What does this toolbox do? Can I use it? What problems can I solve?, etc.
What Does this Toolbox Do?
The Partial Differential Equation (PDE) Toolbox provides a powerful and flexible environment for the study and solution of partial differential equations in two space dimensions and time. The equations are discretized by the Finite Element Method (FEM). The objectives of the PDE Toolbox are to provide you with tools that:
• Define a PDE problem, i.e.
In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author's pioneering text is fully revised and updated to acknowledge many of these developments. It includes a complete treatment of linear multistep methods whilst maintaining its unique and comprehensive emphasis on Runge-Kutta methods and general linear methods.
Although the specialist topics are taken to an advanced level, the entry point to the volume as a whole is not especially demanding.
This volume is an eclectic mix of applications of Monte Carlo methods in many fields of research should not be surprising, because of the ubiquitous use of these methods in many fields of human endeavor. In an attempt to focus attention on a manageable set of applications, the main thrust of this book is to emphasize applications of Monte Carlo simulation methods in biology and medicine.
The goal of this book is to expose the reader to modern computational tools for
solving differential equation models that arise in chemical engineering, e.g.,
diffusion-reaction, mass-heat transfer, and fluid flow. The emphasis is placed
on the understanding and proper use of software packages. In each chapter we
outline numerical techniques that either illustrate a computational property of
interest or are the underlying methods of a computer package. At the close of
each chapter a survey of computer packages is accompanied by examples of
This material is taught in the BSc. Mathematics degree programme at the Manchester Metropolitan University, UK. The Finite Volume Method (FVM) is taught after the Finite Difference Method (FDM) where important concepts such as convergence, consistency and stability are presented. The FDM material is contained in the online textbook, ‘Introductory Finite Difference Methods for PDEs’ which is free to download from:
The three texts in this one cover, entitled ‘The series solution of second order, ordinary differential equations and special
functions’ (Part I), ‘An introduction to Sturm-Liouville theory’ (Part II) and ‘Integral transforms’ (Part III), are three of
the ‘Notebook’ series available as additional and background reading to students at Newcastle University (UK).
Differential evolution is one of the most recent global optimizers. Discovered
in 1995 it rapidly proved its practical efficiency. This book gives you a chance
to learn all about differential evolution. On reading it you will be able to
profitably apply this reliable method to problems in your field.
As for me, my passion for intelligent systems and optimization began as far
back as during my studies at Moscow State Technical University of Bauman,
the best engineering school in Russia. At that time, I was gathering material
for my future thesis.
The present volume, compiled in honor of an outstanding historian of science,
physicist and exceptional human being, Sam Schweber, is unique in assembling
a broad spectrum of positions on the history of science by some of its leading
representatives. Readers will find it illuminating to learn how prominent authors
judge the current status and the future perspectives of their field. Students will find
this volume helpful as a guide in a fragmented field that continues to be dominated
by idiosyncratic expertise and still lacks a methodical canon.
n mathematics, an ordinary differential equation (abbreviated ODE) is an equation containing a function of one independent variable and its derivatives. There are many general forms an ODE can take, and these are classified in practice (see below). The derivatives are ordinary because partial derivatives only apply to functions of many independent variables (see Partial differential equation).
This note deals with two fully parallel methods for solving linear partial differentialalgebraic equations (PDAEs) of the form: Aut + B∆u = f(x, t) where A is a singular, symmetric and nonnegative matrix, while B is a symmetric positive define matrix. The stability and convergence of proposed methods are discussed. Some numerical experiments on high-performance computers are also reported.
We have attempted to write a concise modern treatment of differential equations
emphasizing applications and containing all the core parts of a course in differential
equations.Asemester or quarter course in differential equations is taught to most engineering
students (and many science students) at all universities, usually in the second
year. Some universities have an earlier brief introduction to differential equations and
others do not. Some students will have already seen some differential equations in
their science classes.We do not assume any prior exposure to differential equations.
Introduction to Thermal Analysis Methods analysis refers to a variety of techniques in which physical property of a sample is continuously measured as a function of temperature, whist the sample is subjected to a pre determined temperature profile.
In this chapter you will learn how to draw data flow diagrams, a popular process model that documents a system’s processes and their data flows. You will know process modeling as a systems analysis tool when you can: Define systems modeling and differentiate between logical and physical system models, define process modeling and explain its benefits, recognize and understand the basic concepts and constructs of a process model,...
In this chapter you will learn more about the design phase of systems development. You will know that you understand the process of systems design when you can: Describe the design phase in terms of your information building blocks, identify and differentiate between several systems design strategies, describe the design phase tasks in terms of a computer-based solution for an in-house development project,...
In this chapter you will learn how to design and prototype computer outputs. You will know how to design and prototype outputs when you can: Distinguish between internal, external, and turnaround outputs; differentiate between detailed, summary, and exception reports; identify several output implementation methods; differentiate among tabular, zoned, and graphic formats for presenting information;...
This is the second of two chapters on object-oriented tools and techniques for systems development. This chapter focuses specifically on tools and techniques that are used during systems design. You will know object-oriented systems design when you can: Differentiate between entity, interface, control, persistence, and system classes; understand the concept of a dependency and navigability; define visibility and explain its three levels;...