Atjaunināt sīkdatņu piekrišanu

Financial Mathematics: From Discrete to Continuous Time [Hardback]

(Knox College, Galesburg, Illinois, USA)
  • Formāts: Hardback, 411 pages, height x width: 234x156 mm, weight: 802 g, 109 Line drawings, black and white; 109 Illustrations, black and white
  • Sērija : Chapman and Hall/CRC Financial Mathematics Series
  • Izdošanas datums: 21-Dec-2022
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-10: 1498780407
  • ISBN-13: 9781498780407
Citas grāmatas par šo tēmu:
  • Hardback
  • Cena: 119,73 €
  • Grāmatu piegādes laiks ir 3-4 nedēļas, ja grāmata ir uz vietas izdevniecības noliktavā. Ja izdevējam nepieciešams publicēt jaunu tirāžu, grāmatas piegāde var aizkavēties.
  • Daudzums:
  • Ielikt grozā
  • Piegādes laiks - 4-6 nedēļas
  • Pievienot vēlmju sarakstam
  • Bibliotēkām
Financial Mathematics: From Discrete to Continuous TimePalielināt
  • Formāts: Hardback, 411 pages, height x width: 234x156 mm, weight: 802 g, 109 Line drawings, black and white; 109 Illustrations, black and white
  • Sērija : Chapman and Hall/CRC Financial Mathematics Series
  • Izdošanas datums: 21-Dec-2022
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-10: 1498780407
  • ISBN-13: 9781498780407
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781498780407.html
Keywords:
Financial Mathematics: From Discrete to Continuous Time is a study of the mathematical ideas and techniques that are important to the two main arms of the area of financial mathematics: portfolio optimization and derivative valuation. The text is authored for courses taken by advanced undergraduates, MBA, or other students in quantitative finance programs.

The approach will be mathematically correct but informal, sometimes omitting proofs of the more difficult results and stressing practical results and interpretation. The text will not be dependent on any particular technology, but it will be laced with examples requiring the numerical and graphical power of the machine.

The text illustrates simulation techniques to stand in for analytical techniques when the latter are impractical. There will be an electronic version of the text that integrates Mathematica functionality into the development, making full use of the computational and simulation tools that this program provides. Prerequisites are good courses in mathematical probability, acquaintance with statistical estimation, and a grounding in matrix algebra.

The highlights of the text are:





A thorough presentation of the problem of portfolio optimization, leading in a natural way to the Capital Market Theory Dynamic programming and the optimal portfolio selection-consumption problem through time An intuitive approach to Brownian motion and stochastic integral models for continuous time problems The Black-Scholes equation for simple European option values, derived in several different ways A chapter on several types of exotic options Material on the management of risk in several contexts

Recenzijas

I like Kevin Hastings' "Introduction to Financial Mathematics" (Volume 1) very much.

The book is very readable; it builds slowly with many examples and exercises (and answers to some of the exercises are in the back). The writing style is good; the exercises are easy to understand.



The material is comprehensive and covers the topics well. It is surprising that the book maintains the same clear level of exposition from the simple early chapters to the more complicated later chapters.

The table of contents covers all the material that should appear in a financial mathematics course.

Dan Zwillinger

In addition to its clear explanations, this volume emphasizes real problem solving with examples and exercises that challenge students to apply knowledge of basic concepts to new situations. Another unique aspect is the application of discrete probability to finance; the author provides an overview and illustrates problems in which the rates of interest are random variables, instead of traditional problems that consider only known constants. Topics covered include the mathematics of interest, valuation of bonds, discrete probability for finance, portfolio selection, and derivatives.

This book is highly recommended for undergraduates and those preparing for actuarial credentialing and exams.

S. J. Chapman Jr.,

Purdue University-NorthWest

Preface xiii
Author xvii
1 Review of Preliminaries
1(64)
1.1 Risky Assets
2(9)
1.1.1 Single and Multiple Discrete Time Periods
4(3)
1.1.2 Continuous-Time Processes
7(1)
1.1.3 Martingales
8(3)
1.2 Risk Aversion and Portfolios of Assets
11(7)
1.2.1 Risk Aversion Constant
11(3)
1.2.2 The Portfolio Problem
14(4)
1.3 Expectation, Variance, and Covariance
18(14)
1.3.1 One Variable Expectation
18(4)
1.3.2 Expectation for Multiple Random Variables
22(4)
1.3.3 Variance of a Linear Combination
26(6)
1.4 Simple Portfolio Optimization
32(6)
1.5 Derivative Assets and Arbitrage
38(13)
1.5.1 Futures
38(3)
1.5.2 Arbitrage and Futures
41(4)
1.5.3 Options
45(6)
1.6 Valuation of Derivatives in a Single Time Period
51(14)
1.6.1 Replicating Portfolios
52(6)
1.6.2 Risk-Neutral Valuation
58(7)
2 Portfolio Selection and CAPM Theory
65(88)
2.1 Portfolio Optimization with Multiple Assets
65(17)
2.1.1 Lagrange Multipliers
69(2)
2.1.2 Qualitative Behavior
71(2)
2.1.3 Correlated Assets
73(3)
2.1.4 Portfolio Separation and the Market Portfolio
76(6)
2.2 Capital Market Theory, Part I
82(17)
2.2.1 Linear Algebraic Approach
82(5)
2.2.2 Efficient Mean-Standard Deviation Frontier
87(12)
2.3 Capital Market Theory, Part II
99(15)
2.3.1 Capital Market Line
99(5)
2.3.2 CAPM Formula; Asset β
104(4)
2.3.3 Systematic and Non-Systematic Risk; Pricing Using CAPM
108(6)
2.4 Utility Theory
114(22)
2.4.1 Securities and Axioms for Investor Behavior
114(4)
2.4.2 Indifference Curves, Certainty Equivalent, Risk Aversion
118(5)
2.4.3 Examples of Utility Functions
123(4)
2.4.4 Absolute and Relative Risk Aversion
127(2)
2.4.5 Utility Maximization
129(7)
2.5 Multiple Period Portfolio Problems
136(17)
2.5.1 Problem Description and Dynamic Programming Approach
136(2)
2.5.2 Examples
138(10)
2.5.3 Optimal Portfolios and Martingales
148(5)
3 Discrete-Time Derivatives Valuation
153(108)
3.1 Options Pricing for Multiple Time Periods
153(18)
3.1.1 Introduction
153(3)
3.1.2 Valuation by Chaining
156(7)
3.1.3 Valuation by Martingales
163(8)
3.2 Key Ideas of Discrete Probability, Part I
171(14)
3.2.1 Algebras and Measurability
172(9)
3.2.2 Independence
181(4)
3.3 Key Ideas of Discrete Probability, Part II
185(17)
3.3.1 Conditional Expectation
185(11)
3.3.2 Application to Pricing Models
196(6)
3.4 Fundamental Theorems of Options Pricing
202(21)
3.4.1 The Market Model
203(5)
3.4.2 Gain, Arbitrage, and Attainability
208(4)
3.4.3 Martingale Measures and the Fundamental Theorems
212(11)
3.5 Valuation of Non-Vanilla Options
223(20)
3.5.1 American and Bermudan Options
223(9)
3.5.2 Barrier Options
232(5)
3.5.3 Asian Options
237(1)
3.5.4 Two-Asset Derivatives
238(5)
3.6 Derivatives Pricing by Simulation
243(10)
3.6.1 Setup and Algorithm
243(3)
3.6.2 Examples
246(7)
3.7 From Discrete to Continuous Time (A Preview)
253(8)
4 Continuous Probability Models
261(74)
4.1 Continuous Distributions and Expectation
261(13)
4.1.1 Densities and Cumulative Distribution Functions
261(4)
4.1.2 Expectation
265(3)
4.1.3 Normal and Lognormal Distributions
268(6)
4.2 Joint Distributions
274(21)
4.2.1 Basic Ideas
274(4)
4.2.2 Marginal and Conditional Distributions
278(4)
4.2.3 Independence
282(2)
4.2.4 Covariance and Correlation
284(4)
4.2.5 Bivariate Normal Distribution
288(7)
4.3 Measurability and Conditional Expectation
295(14)
4.3.1 Sigma Algebras
295(3)
4.3.2 Random Variables and Measurability
298(2)
4.3.3 Continuous Conditional Expectation
300(9)
4.4 Brownian Motion and Geometric Brownian Motion
309(15)
4.4.1 Random Walk Processes
310(2)
4.4.2 Standard Brownian Motion
312(2)
4.4.3 Non-Standard Brownian Motion
314(3)
4.4.4 Geometric Brownian Motion
317(3)
4.4.5 Brownian Motion and Binomial Branch Processes
320(4)
4.5 Introduction to Stochastic Differential Equations
324(11)
4.5.1 Meaning of the General SDE
325(2)
4.5.2 Ito's Formula
327(3)
4.5.3 Geometric Brownian Motion as Solution
330(5)
5 Derivative Valuation in Continuous Time
335(50)
5.1 Black-Scholes Via Limits
335(10)
5.1.1 Black-Scholes Formula
335(1)
5.1.2 Limiting Approach
336(5)
5.1.3 Put Options and Put-Call Parity
341(4)
5.2 Black-Scholes Via Martingales
345(15)
5.2.1 Trading Strategies and Martingale Valuation
345(2)
5.2.2 Martingale Measures
347(4)
5.2.3 Asset and Bond Binaries
351(4)
5.2.4 Other Binary Derivatives
355(5)
5.3 Black-Scholes Via Differential Equations
360(7)
5.3.1 Deriving the PDE
360(3)
5.3.2 Boundary Conditions; Solving the PDE
363(4)
5.4 Checking Black-Scholes Assumptions
367(18)
5.4.1 Normality of Rates of Return
368(8)
5.4.2 Stability of Parameters
376(2)
5.4.3 Independence of Rates of Return
378(7)
A Multivariate Normal Distribution
385(10)
A.1 Review of Matrix Concepts
385(2)
A.2 Multivariate Normal Distribution
387(8)
B Answers to Selected Exercises
395(10)
Bibliography 405(2)
Index 407
Kevin J. Hastings is Professor of Mathematics; Rothwell C. Stephens Distinguished Service Chair at Knox College. He holds a Ph.D. from Northwestern University. His interests include applications to real-world problems affected by random inputs or disturbances. He is the author or three other books for CRC Press:

Introduction to Financial Mathematics, CRC Press, 2016. CHOICE Highly Recommended selection and 2017 Top Books for Colleges.

Introduction to Probability with Mathematica, 2nd ed., Chapman & Hall/CRC Press, 2009.

Introduction to the Mathematics of Operations Research with Mathematica, 2nd edition, Taylor & Francis/Marcel Dekker, 2006.

Introduction to Probability with Mathematica. CRC Press/Chapman & Hall, 2000. Also available as an e-book.