Series: Probability and its Applications
2008, Approx. 350 p., Softcover
ISBN: 978-1-84800-002-5
Due: December 2007
About this book
Until now, solved examples of the application of stochastic control to actuarial problems could only be found in journals - this will be the first book to systematically present these methods in one volume.
The author starts with a short introduction to stochastic control techniques, both in discrete and continuous time. Then he applies the principles to several problems in actuarial methematics. These examples show how verification theorems and existence theorems may be proved - they also show that, in contrast to general belief, the non-diffusion case is simpler than the diffusion case. In the last part of the book, applied probability techniques are used to determine the asymptotics of the controlled stochastic process.
Stochastic Control in Insurance also includes a number of appendices to supplement the main material of the book - and will be suitable for graduate and postgraduate students of actuarial and financial mathematics, as well as researchers, and practitioners in insurance companies and banks who wish to use these techniques in their work.
Table of contents
Stochastic Control in Discrete Time.- Stochastic Control in Continuous Time.- Problems in Life Insurance.- Asymptotics of Controlled Risk Processes.- Asymptotics of Characteristics under Optimal Control.- Appendices.- Stochastic Processes and Martingales.- Markov Processes and Generators.- Change of Measure Techniques.- Risk Theory.- The Black-Scholes Model.- Life Insurance
Series: Graduate Texts in Mathematics , Vol. 95/1
Originally published in one volume
2008, XII, 520 p. 47 illus., Hardcover
ISBN: 978-0-387-72205-4
Due: December 2007
About this textbook
Successfully synthesizes the most important classical ideas and results with many of the major achievements of modern probability theory
Author provides clear and comprehensive introduction to probability theory
This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks, martingales, Markov chains, ergodic theory, weak convergence of probability measures, stationary stochastic processes, and the Kalman-Bucy filter. Many examples are discussed in detail, and there are a large number of exercises. The book is accessible to advanced undergraduates and can be used as a text or for self-study.
The third edition contains new problems and exercises, new proofs, expanded material on financial mathematics, financial engineering, and mathematical statistics, and a final chapter on the history of probability theory.
Table of contents
Preface to the Third Edition.- Preface to the Second Edition.- Preface to the First Edition.- Introduction.- Elementary Probability Theory.- Mathematical Foundations of Probability Theory.- Proximity and Convergence of Probability Measures.- Central Limit Theorem.- Bibliography.- Index.
Series: Graduate Texts in Mathematics , Vol. 95/2
Originally published in one volume
2008, Approx. 430 p., Hardcover
ISBN: 978-0-387-72207-8
Due: December 2007
About this textbook
Successfully synthesizes all of the classical ideas and results with many of the major achievements of modern probability theory
Author provides clear and comprehensive introduction to probability theory
This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks, martingales, Markov chains, ergodic theory, weak convergence of probability measures, stationary stochastic processes, and the Kalman-Bucy filter. Many examples are discussed in detail, and there are a large number of exercises. The book is accessible to advanced undergraduates and can be used as a text or for self-study.
The third edition contains new problems and exercises, new proofs, expanded material on financial mathematics, financial engineering, and mathematical statistics, and a final chapter on the history of probability theory.
Table of contents
Preface.- Sequences and Sums of Independent Random Variables.- Stationary (Strict Sense) Random Sequences and Ergodic Theory.- Stationary (Wide Sense) Random Sequences.- L2 Theory.- Sequences of Random Variables that Form Martingales.- Sequences of Random Variables that Form Markov Chains.- History of Mathematical Theory of Probability.- Bibliography (Chapters IV-VIII).- List of Literature.- Index.
Series: Undergraduate Texts in Mathematics
2008, Approx. 570 p., Hardcover
ISBN: 978-0-387-74527-5
Due: January 2008
About this textbook
This book is an informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials. A strong emphasis on congruence classes leads in a natural way to finite groups and finite fields. The new examples and theory are built in a well-motivated fashion and made relevant by many applications - to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises, ranging from routine examples to extensions of theory, are found throughout the book; hints and answers for many of them are included in an appendix.
gAt every stage, a wide variety of applications is presented...The user-friendly exposition is appropriate for the intended audience.h
T.W. Hungerford
The new edition will contain topics such as Luhn's formula, homomorphisms, detaching coefficients, and more.
Table of contents
Numbers.- Induction.- Euclid's Algorithm.- Unique Factorization.- Congruences.- Congruence Classes.- Applications of Congruences.- Rings and Fields.- Fermat's and Euler's Theorems.- Applications of Fermat's and Euler's Theorems.- On Groups.- The Chinese Remainder Theorem.- Matrices and Codes.- Polynomials.- Unique Factorization.- The Fundamental Theorem of Algebra.- Derivatives.- Factoring in QAxU,I.- The Binomial Theorem in Characteristic p.- Congruences and the Chinese Remainder Theorem.- Applications of the Chinese Remainder Theorem.- Factoring in FpAxU and in ZAxU.- Primitive Roots.- Cyclic Groups and Primitive Roots.- Pseudoprimes.- Roots of Unity in Z/mZ.- Quadratic Residues.- Congruence Classes Mopdulo a Polynomial.- Some Applications of Finite Fields.- Classifying Finite Fields.