Mastering Mathematical Finance
MAST ERING
MATH EMAT ICAL
FINAN CE
Stochastic Interest Rates NER NEY DAR AGH MCI AWN IAK TOM ASZ ZAST
General Editors: Marek Capiński, University of Science and Technology, Krakow; Ekkehard Kopp, University of Hull; Tomasz Zastawniak, University of York
MASTERING MATHEMATICAL FINANCE
The Black–Scholes Model ´ MAREK CAPINSKI EKKEHARD KOPP
Results are proved carefully, and the key concepts are motivated by concrete examples drawn from financial market models. Students can test their understanding through the large number of exercises that are integral to the text.
• Key concepts of probability are developed directly in the context of financial models • Careful motivation and plentiful exercises help students gain confidence • Solutions to exercises are available online
Mastering Mathematical Finance (MMF) is a series of short books that cover all core topics and the most common electives offered in Master’s programmes in mathematical or quantitative finance. The books are closely coordinated and largely self-contained, and can be used efficiently in combination but also individually.
MASTERING MATHEMATIC AL FINANCE
Probability for Finance
Probability for Finance
Kopp 9780521175579 Cover. C M Y K
A series of short books that cover all the core topics and the most common electives offered in master’s programs in mathematical/quantitative finance. The books are closely coordinated but each self-contained, so that they can be used efficiently in combination but also individually.
kopp, malczak & zastawniak
Students and instructors alike will benefit from this rigorous, unfussy text, which keeps a clear focus on the basic probabilistic concepts required for an understanding of financial market models, including independence and conditioning. Assuming only some calculus and linear algebra, the text applies key results of measure and integration to probability spaces and random variables, culminating in Central Limit Theory. Consequently, it provides essential pre-requisites to graduate-level study of modern finance and, more generally, to the study of stochastic processes.
The MMF books start financially from scratch and mathematically assume only undergraduate calculus, linear algebra and elementary probability theory. The necessary mathematics is developed rigorously, with emphasis on a natural development of mathematical ideas and financial intuition, and the readers quickly see real-life financial applications, both for motivation and as the ultimate end for the theory. All books are written for both teaching and self-study, with worked examples, exercises and solutions.
ekkehard kopp is Emeritus Professor of Mathematics at the University of Hull. He has published over 50 research papers and five books, on measure and probability, stochastic analysis and mathematical finance. He has taught in the UK, Canada and South Africa, and he serves on the editorial board of the AIMS Library Series. jan malczak has published over 20 research papers and taught courses in analysis, differential equations, measure and probability, and the theory of stochastic differential processes. He is currently Professor of Mathematics at AGH University of Science and Technology in Kraków, Poland. tomasz zastawniak holds the Chair of Mathematical Finance at the University of York. He has authored about 50 research publications and four books. He has supervised four PhD dissertations and around 80 MSc dissertations in mathematical finance.
EKKEHARD KOPP JAN MALCZAK TOMASZ ZASTAWNIAK
cMyk
PPc.
International Series on Actuarial Science
Solutions Manual for Actuarial Mathematics for Life Contingent Risks
Actuarial Mathematics for t Life Contingen Risks
Solutions Manual for Actuarial Mathematics for Life Contingent Risks SECOND EDITION
David C. M. Dickson, Mary R. Hardy and Howard R. Waters
ON SECON D EDITI
on, Mary R. Hardy David C. M. Dicks Waters and Howard R.
and valuation.’ Journal Scandinavian Actuarial
Cover designed
by Hart McLeod
Ltd
PPC. C M Y BLK
SWEETING: FINANCIAL ENTERPRISE.
The tools of modelling and simulation are outlined in Part I with special emphasis on the Monte Carlo method and its use. Part II deals with general insurance and Part III with life insurance and financial risk. Algorithms that can be implemented on any programming platform are spread throughout, and a program library written in R is included. Numerous figures and experiments with R code illustrate the text. The author’s non-technical approach is ideal for graduate students, the only prerequisites being introductory courses in calculus and linear algebra, probability and statistics. The book will also be useful for actuaries and other analysts in the industry looking to update their skills.
Cover designed by Hart McLeod Ltd
Predictive Modeling Applications in Actuarial Science Volume I: Predictive Modeling Techniques Edited by
Edward W. Frees, Richard A. Derrig, Glenn Meyers
Computation and Modelling in Insurance and Finance
Scientific computing is as critical for the analysis of risk in insurance and finance as are mathematics and statistics, and it should be taught jointly with them. This book offers such an integrated approach at an introductory level and provides readers with much of what is needed in practice, including how simulation programs are designed, used and reused (with modifications) as situations change. Complex problems with risk from many sources are discussed, as is the sensitivity of conclusions on assumptions and historical data.
International Series on Actuarial Science
Bølviken
The International Series on Actuarial Science, published by Cambridge University Press in conjunction with the Institute and Faculty of Actuaries, contains textbooks for students taking courses in or related to actuarial science, as well as more advanced works designed for continuing professional development or for describing and synthesizing research. The series is a vehicle for publishing books that reflect changes and developments in the curriculum, that encourage the introduction of courses on actuarial science in universities, and that show how actuarial science can be used in all areas where there is long-term financial risk.
www.cambridge.org/isas
SECOND EDITION
9781107044074. & Waters – Dickson, HarDy
This must-have manual provides detailed solutions to all of the 200+ exercises in Dickson, Hardy and Waters’ Actuarial Mathematics for Life Contingent Risks, Second Edition. This ground-breaking text on the modern mathematics of life insurance is required reading for the Society of Actuaries’ Exam MLC and also provides a solid preparation for the life contingencies material of the UK actuarial profession’s Exam CT5. Beyond the professional examinations, the textbook and solutions manual offer readers the opportunity to develop insight and understanding, and also offer practical advice for solving problems using straightforward, intuitive numerical methods. Companion spreadsheets illustrating al Science Actuari onthese techniques are available for free download.
Dickson, Hardy and Waters
It may be an and easy to read. written, well organized, programmes ‘The book is well ate and graduate for both undergradu information for excellent textbook source of useful It is also a rich managers in actuarial science. and financial risk the actuarial profession flow modelling practitioners of to liability cash and inspiring guide who seek a practical
SECOND EDITION
Editorial Board: Christopher Daykin, Independent Consultant and Actuary; Angus Macdonald, Heriot-Watt University
International Series
matics for Actuarial Mathe Risks Life Contingent
and risk structures for the products actuarial best equip themselves three leaders in How can actuaries aking textbook, this ground-bre es. of the future? In life contingenci perspective on emphasizing practical science give a modern models and theory, a with actuarial authors then develop The book begins techniques. The computational models, emerging applications using multiple state ry outlook, introducing contains more edition more contempora This expanded well as embedded options. preparation as cash flows and to help with exam chapters exercises designed new sections and brand examples and are on expertise. There joint lives and developing up-to-date on models involving Markov processes, insurance. on discrete time traditional g and participatin this g applications, Universal Life insurance and emphasizin with intuition, wishing Balancing rigour for qualified actuaries for university courses, preparing for the textbook is ideal for individuals their skills and or Institute to renew and update the Society of Actuaries examinations of syllabus and entire SOA MLC professional actuarial book covers the Actuaries. The new, long and Faculty of preparing for the valuable for students will be especially answer exam questions.
Dickson, Hardy and Waters
International Series on Actuarial Science
9781107620261 DICKSON – SOlutIONS MaNual fOr aCtuarIal MatheMatICS fOr lIfe CONtINgeNt rISKS C M Y K
www.cambridge.org/mmf
International Series on Actuarial Science
Computation and Modelling in Insurance and Finance Erik Bølviken