Financial Mathematics for Actuaries (3版)

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Financial Mathematics for Actuaries 作 / 譯 者 ： Wai-Sum Chan,Yiu-Kuen Tse I S B N - 13 ： 9789811245671 I S B N - 10 ： 9811245673 類 別： 財務其他 版 次： 3 版 年 份： 2022 規 格： 345 頁 出 版 商： World Scientific Publishing 內容簡介 This book provides a thorough understanding of the fundamental concepts of financial mathematics essential for the evaluation of any financial product and instrument. Mastering concepts of present and future values of streams of cash flows under different interest rate environments is core for actuaries and financial economists. This book covers the body of knowledge required by the Society of Actuaries (SOA) for its Financial Mathematics (FM) Exam. The third edition includes major changes such as an addition of an "R Laboratory" section in each chapter, except for Chapter 9. These sections provide R codes to do various computations, which will facilitate students to apply conceptual knowledge. Additionally, key definitions have been revised and the theme structure has been altered. Students studying undergraduate courses on financial mathematics for actuaries will find this book useful. This book offers numerous examples and exercises, some of which are adapted from previous SOA FM Exams. It is also useful for students preparing for the actuarial professional exams through self-study. 目錄 Ch 1 Interest Accumulation and Time Value of Money Ch 2 Annuities Ch 3 Spot Rates, Forward Rates and the Term Structure Ch 4 Rates of Return Ch 5 Loans and Costs of Borrowing Ch 6 Bonds and Bond Pricing Ch 7 Bond Yields and the Term Structure Ch 8 Bond Management Ch 9 Interest Rates and Financial Securities Ch10 Stochastic Interest Rates

Introductory Course on Financial Mathematics

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This book is an elementary introduction to the basic concepts of financial mathematics with a central focus on discrete models and an aim to demonstrate simple, but widely used, financial derivatives for managing market risks. Only a basic knowledge of probability, real analysis, ordinary differential equations, linear algebra and some common sense are required to understand the concepts considered in this book. Financial mathematics is an application of advanced mathematical and statistical methods to financial management and markets, with a main objective of quantifying and hedging risks. Since the book aims to present the basics of financial mathematics to the reader, only essential elements of probability and stochastic analysis are given to explain ideas concerning derivative pricing and hedging. To keep the reader intrigued and motivated, the book has a ‘sandwich’ structure: probability and stochastics are given in situ where mathematics can be readily illustrated by application to finance. The first part of the book introduces one of the main principles in finance — ‘no arbitrage pricing’. It also introduces main financial instruments such as forward and futures contracts, bonds and swaps, and options. The second part deals with pricing and hedging of European- and American-type options in the discrete-time setting. In addition, the concept of complete and incomplete markets is discussed. Elementary probability is briefly revised and discrete-time discrete-space stochastic processes used in financial modelling are considered. The third part introduces the Wiener process, Ito integrals and stochastic differential equations, but its main focus is the famous Black–Scholes formula for pricing European options. Some guidance for further study within this exciting and rapidly changing field is given in the concluding chapter. There are approximately 100 exercises interspersed throughout the book, and solutions for most problems are provided in the appendices. Sample Chapter(s) Historical Remarks (180 KB) Bonds and Swaps (490 KB) Binary Model of Price Evolution (394 KB) Connection to 'Reality' (289 KB) Request Inspection Copy Contents: Historical Remarks Financial Instruments and Arbitrage: Preliminary Examples Forwards, Futures and Arbitrage Bonds and Swaps European Options Problems for Part I Discrete-Time Stochastic Modelling and Option Pricing: Binary Model of Price Evolution Elements of Probability Theory Discrete-Time Stochastic Processes Multiperiod Binary Tree Model Complete and Incomplete Markets American Options Problems for Part II Continuous-Time Stochastic Modelling and the Black—Scholes Formula: Connection to 'Reality' Probabilistic Model for an Experiment with Infinitely Many Outcomes Limit of the Discrete-Price Model and Price of a European Option in the Continuous-Time Case Brownian Motion (Wiener Process) Simplistic Introduction to Ito Calculus Problems for Part III Further Study Appendix: Solutions Readership: Undergraduate and postgraduate students taking a course in financial mathematics.

Theory of Stochastic Processes: with Applications to Financial Mathematics and Risk Theory

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Providing the necessary materials within a theoretical framework, this volume presents stochastic principles and processes, and related areas. Over 1000 exercises illustrate the concepts discussed, including modern approaches to sample paths and optimal stopping.