Presents the mathematical methods required for pricing financial derivatives
Encourages hands-on experience and builds intuition by explaining theoretical concepts with computer simulations
Covers mathematical prerequisites, including measure theory, ordinary differential equations, and partial differential equations
This book is an introduction to stochastic analysis and quantitative finance; it includes both theoretical and computational methods. Topics covered are stochastic calculus, option pricing, optimal portfolio investment, and interest rate models. Also included are simulations of stochastic phenomena, numerical solutions of the Black?Scholes?Merton equation, Monte Carlo methods, and time series. Basic measure theory is used as a tool to describe probabilistic phenomena.
The level of familiarity with computer programming is kept to a minimum. To make the book accessible to a wider audience, some background mathematical facts are included in the first part of the book and also in the appendices. This work attempts to bridge the gap between mathematics and finance by using diagrams, graphs and simulations in addition to rigorous theoretical exposition. Simulations are not only used as the computational method in quantitative finance, but they can also facilitate an intuitive and deeper understanding of theoretical concepts.
Stochastic Analysis for Finance with Simulations is designed for readers who want to have a deeper understanding of the delicate theory of quantitative finance by doing computer simulations in addition to theoretical study. It will particularly appeal to advanced undergraduate and graduate students in mathematics and business, but not excluding practitioners in finance industry.
* Provides a comprehensive introduction to module theory with clear
explanations
* Complements results on CS-modules and CS-rings from former
monographs addressing this trend
* Presents cutting-edge research on generalizations of CS-modules
and CS-rings
* Features a wealth of examples and open problems
The main focus of this monograph is to offer a comprehensive presentation of known
and new results on various generalizations of CS-modules and CS-rings. Extending (or
CS) modules are generalizations of injective (and also semisimple or uniform) modules.
While the theory of CS-modules is well documented in monographs and textbooks, results
on generalized forms of the CS property as well as dual notions are far less present in the
literature.
With their work the authors provide a solid background to module theory, accessible to
anyone familiar with basic abstract algebra. The focus of the book is on direct sums of CSmodules
and classes of modules related to CS-modules, such as relative (injective) ejective
modules, (quasi) continuous modules, and lifting modules. In particular, matrix CS-rings
are studied and clear proofs of fundamental decomposition results on CS-modules over
commutative domains are given, thus complementing existing monographs in this area.
Open problems round out the work and establish the basis for further developments in
the field. The main text is complemented by a wealth of examples and exercises.
1st ed. 2016, Approx. 370 p.
A product of Birkhauser Basel
Printed book
Softcover
ISBN 978-3-0348-0950-4
This book is devoted to review two of the most relevant approaches to the study of classical field theories of the first order, say k-symplectic and k-cosymplectic geometry. This approach is also compared with others like multisymplectic formalism.
It will be very useful for researchers working in classical field theories and graduate students interested in developing a scientific career in the subject.
A Review of Hamiltonian and Lagrangian Mechanics:
Hamiltonian and Lagrangian Mechanics
k-Symplectic Formulation of Classical Field Theories:
k-Symplectic Geometry
k-Symplectic Formalism
Hamiltonian Classical Field Theory
Hamilton?Jacobi Theory in k-Symplectic Field Theories
Lagrangian Classical Field Theories
Examples
k-Cosymplectic Formulation of Classical Field Theories:
k-Cosymplectic Geometry
k-Cosymplectic Formalism
Hamiltonian Classical Field Theories
Hamilton?Jacobi Equation
Lagrangian Classical Field Theories
Examples
k-Symplectic Systems versus Autonomous k-Cosymplectic Systems
Relationship between k-Symplectic and k-Cosymplectic Approaches and the Multisymplectic Formalism:
Multisymplectic Formalism
Appendices:
Symplectic Manifolds
Cosymplectic Manifolds
Glossary of Symbols
Readership: Graduate students and researchers in classical field theories.
224pp Sep 2015
ISBN: 978-981-4699-75-4 (hardcover)
Real analysis provides the fundamental underpinnings for calculus, arguably the most useful and influential mathematical idea ever invented. It is a core subject in any mathematics degree, and also one which many students find challenging. A Sequential Introduction to Real Analysis gives a fresh take on real analysis by formulating all the underlying concepts in terms of convergence of sequences. The result is a coherent, mathematically rigorous, but conceptually simple development of the standard theory of differential and integral calculus ideally suited to undergraduate students learning real analysis for the first time.
This book can be used as the basis of an undergraduate real analysis course, or used as further reading material to give an alternative perspective within a conventional real analysis course.
Basic Properties of the Set or Real Numbers
Real Sequences
Limit Theorems
Subsequences
Series
Continuous Functions
Some Symbolic Logic
Limits of Functions
Differentiable Functions
Power Series
Integration
Logarithms and Irrational Powers
What are the Reals?
Readership: Undergraduate mathematics students taking a course in real analysis.
270pp Dec 2015
ISBN: 978-1-78326-782-8 (hardcover)
USD75.00 Buy Now
ISBN: 978-1-78326-783-5 (softcover)
This is a book on path integrals which provides a quick and swift description of the topic. It contains original material that never before has appeared in a book. The new topics include the path integrals for the Wigner functions and for Classical Mechanics.
Quantum Mechanics and Summing Up Amplitudes
Double Slit Experiment
Infinite Slits Experiments and Path-Correspondence
Dirac's 1932 Paper on Small Time Amplitudes
Time-Slicing: From Infinitesimal to Finite Time Intervals
Re-derivation of the Feynman Path Integrals via the Trotter Formula
Free-Particle Propagator
Continuous Paths but Nowhere Differentiable
Path Integrals for Quadratic Potentials
WKB in the Operatorial Language
WKB in the Path-Integral Language
Introduction to the Formalism of Wigner Functions
Marinov's Path Integral for Wigner Functions
Semiclassical Expansion of Marinov's Work
The Work of Koopman and von Neumann (KvN) on the Operatorial Version of Classical Mechanics
Path Integral for Classical Mechanics (CPI) from the KvN Formalism
Cartan Calculus via the CPI
Geometric Quantization via the CPI
Non-Superposition Principle in Classical Mechanics and Degrees of Freedom
Going Beyond Classical Mechanics
Readership: Student and professional in quantum and classical mechanics.
140pp Jan 2016
ISBN: 978-981-4603-92-8 (hardcover)
ISBN: 978-981-4603-93-5 (softcover)