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Applied Probabilistic Calculus for Financial Engineering

Book Description

Illustrates how R may be used successfully to solve problems in quantitative finance

Applied Probabilistic Calculus for Financial Engineering: An Introduction Using R provides R recipes for asset allocation and portfolio optimization problems. It begins by introducing all the necessary probabilistic and statistical foundations, before moving on to topics related to asset allocation and portfolio optimization with R codes illustrated for various examples. This clear and concise book covers financial engineering, using R in data analysis, and univariate, bivariate, and multivariate data analysis. It examines probabilistic calculus for modeling financial engineering—walking the reader through building an effective financial model from the Geometric Brownian Motion (GBM) Model via probabilistic calculus, while also covering Ito Calculus. Classical mathematical models in financial engineering and modern portfolio theory are discussed—along with the Two Mutual Fund Theorem and The Sharpe Ratio. The book also looks at R as a calculator and using R in data analysis in financial engineering. Additionally, it covers asset allocation using R, financial risk modeling and portfolio optimization using R, global and local optimal values, locating functional maxima and minima, and portfolio optimization by performance analytics in CRAN.

  • Covers optimization methodologies in probabilistic calculus for financial engineering
  • Answers the question: What does a "Random Walk" Financial Theory look like?
  • Covers the GBM Model and the Random Walk Model
  • Examines modern theories of portfolio optimization, including The Markowitz Model of Modern Portfolio Theory (MPT), The Black-Litterman Model, and The Black-Scholes Option Pricing Model

Applied Probabilistic Calculus for Financial Engineering: An Introduction Using R s an ideal reference for professionals and students in economics, econometrics, and finance, as well as for financial investment quants and financial engineers.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Dedication
  5. Preface
  6. About the Companion Website
  7. Chapter 1: Introduction to Financial Engineering
    1. 1.1 What Is Financial Engineering?
    2. 1.2 The Meaning of the Title of This Book
    3. 1.3 The Continuing Challenge in Financial Engineering
    4. 1.4 “Financial Engineering 101”: Modern Portfolio Theory
    5. 1.5 Asset Class Assumptions Modeling
    6. 1.6 Some Typical Examples of Proprietary Investment Funds
    7. 1.7 The Dow Jones Industrial Average (DJIA) and Inflation
    8. 1.8 Some Less Commendable Stock Investment Approaches
    9. 1.9 Developing Tools for Financial Engineering Analysis
    10. Review Questions
  8. Chapter 2: Probabilistic Calculus for Modeling Financial Engineering
    1. 2.1 Introduction to Financial Engineering
    2. 2.2 Mathematical Modeling in Financial Engineering
    3. 2.3 Building an Effective Financial Model from GBM via Probabilistic Calculus
    4. 2.4 A Continuous Financial Model Using Probabilistic Calculus: Stochastic Calculus, Ito Calculus
    5. 2.5 A Numerical Study of the Geometric Brownian Motion (GBM) Model and the Random Walk Model Using R
    6. Review Questions and Exercises
  9. Chapter 3: Classical Mathematical Models in Financial Engineering and Modern Portfolio Theory
    1. 3.1 An Introduction to the Cost of Money in the Financial Market
    2. 3.2 Modern Theories of Portfolio Optimization
    3. 3.3 The Black–Litterman Model
    4. 3.4 The Black–Scholes Option Pricing Model
    5. 3.5 The Black–Litterman Model
    6. 3.6 The Black–Litterman Model
    7. 3.7 The Black–Scholes Option Pricing Model
    8. 3.8 Some Worked Examples
    9. Review Questions and Exercises
    10. Solutions to Exercise 3: The Black-Scholes Equation
  10. Chapter 4: Data Analysis Using R Programming
    1. 4.1 Data and Data Processing
    2. Review Questions for Section 4.1
    3. 4.2 Beginning R
    4. Review Questions for Section 4.2
    5. 4.3 R as a Calculator
    6. Review Questions for Section 4.3
    7. Exercises for Section 4.3
    8. 4.4 Using R in Data Analysis in Financial Engineering
    9. Review Questions for Section 4.4
    10. 4.5 Univariate, Bivariate, and Multivariate Data Analysis
    11. Review Questions for Section 4.5
    12. Exercise for Section 4.5
  11. Chapter 5: Assets Allocation Using R
    1. 5.1 Risk Aversion and the Assets Allocation Process
    2. 5.2 Classical Assets Allocation Approaches
    3. 5.3 Allocation with Time Varying Risk Aversion
    4. 5.4 Variable Risk Preference Bias
    5. 5.5 A Unified Approach for Time Varying Risk Aversion
    6. 5.6 Assets Allocation Worked Examples
    7. Review Questions and Exercises
  12. Chapter 6: Financial Risk Modeling and Portfolio Optimization Using R
    1. 6.1 Introduction to the Optimization Process
    2. 6.2 Optimization Methodologies in Probabilistic Calculus for Financial Engineering
    3. 6.3 Financial Risk Modeling and Portfolio Optimization
    4. 6.4 Portfolio Optimization Using R1
    5. Review Questions and Exercises
  13. References
  14. Index
  15. End User License Agreement