Chapter
1.6 Some Typical Examples of Proprietary Investment Funds
1.7 The Dow Jones Industrial Average (DJIA) and Inflation
1.8 Some Less Commendable Stock Investment Approaches
1.8.2 Algorithmic Trading
1.9 Developing Tools for Financial Engineering Analysis
2: Probabilistic Calculus for Modeling Financial Engineering
2.1 Introduction to Financial Engineering
2.1.1 Some Classical Financial Data
2.2 Mathematical Modeling in Financial Engineering
2.2.1 A Discrete Model versus a Continuous Model
2.2.2 A Deterministic Model versus a Probabilistic Model
2.2.2.1 Calculus of the Deterministic Model
2.2.2.2 The Geometric Brownian Motion (GBM) Model and the Random Walk Model
2.2.2.3 What Does a ``Random Walk´´ Financial Theory Look Like?
2.3 Building an Effective Financial Model from GBM via Probabilistic Calculus
2.3.1 A Probabilistic Model for the Stock Market
2.3.2 Probabilistic Processes for the Stock Market Entities
2.3.3 Mathematical Modeling of Stock Prices
2.4 A Continuous Financial Model Using Probabilistic Calculus: Stochastic Calculus, Ito Calculus
2.4.1 A Brief Observation of the Geometric Brownian Motion
2.5 A Numerical Study of the Geometric Brownian Motion (GBM) Model and the Random Walk Model Using R
2.5.1 Modeling Real Financial Data
2.5.1.1 The Geometric Brownian Motion (GBM) Model and the Random Walk Model
2.5.1.2 Other Models for Simulating Random Walk Systems Using R
2.5.2 Some Typical Numerical Examples of Financial Data Using R
3: Classical Mathematical Models in Financial Engineering and Modern Portfolio Theory
3.1 An Introduction to the Cost of Money in the Financial Market
3.2 Modern Theories of Portfolio Optimization
3.2.1 The Markowitz Model of Modern Portfolio Theory (MPT)
3.2.1.1 Risk and Expected Return
3.2.1.3 Efficient Frontier with No Risk-Free Assets
3.2.1.4 The Two Mutual Fund Theorem
3.2.1.5 Risk-Free Asset and the Capital Allocation Line
3.2.1.7 The Capital Allocation Line (CAL)
3.2.1.9 Specific and Systematic Risks
3.2.2 Capital Asset Pricing Model (CAPM)
3.2.2.1 The Security Characteristic Line (SCL)
3.2.3 Some Typical Simple Illustrative Numerical Examples of the Markowitz MPT Using R
3.2.3.1 Markowitz MPT Using R: A Simple Example of a Portfolio Consisting of Two Risky Assets
3.2.3.2 Evaluating a Portfolio
3.2.4 Management of Portfolios Consisting of Two Risky Assets
3.2.4.1 The Global Minimum-Variance Portfolio
3.2.4.2 Effects of Portfolio Variance on Investment Possibilities
3.2.4.3 Introduction to Portfolio Optimization
3.2.5 Attractive Portfolios with Risk-Free Assets
3.2.5.1 An Attractive Portfolio with a Risk-Free Asset
3.2.5.2 The Tangency Portfolio
3.2.5.3 Computing for Tangency Portfolios
3.2.6 The Mutual Fund Separation Theorem
3.2.7 Analyses and Interpretation of Efficient Portfolios
3.3 The Black-Litterman Model
3.4 The Black-Scholes Option Pricing Model
3.5 The Black-Litterman Model
3.6 The Black-Litterman Model
3.6.1 Derivation of the Black-Litterman Model
3.6.1.1 Derivation Using Theil's Mixed Estimation
3.6.1.2 Derivation Using Bayes' Theory
3.6.2 Further Discussions on The Black-Litterman Model
3.6.2.1 An Alternative Formulation of the Black-Litterman Formula
3.6.2.2 A Fundamental Relationship: rA ∼ N{Π, (1 + τ)Σ}
3.6.2.3 On Implementing the Black-Litterman Model
3.7 The Black-Scholes Option Pricing Model
4: Data Analysis Using R Programming
4.1 Data and Data Processing
4.2.1 A First Session Using R
4.2.2 The R Environment - This is Important!
4.3.1 Mathematical Operations Using R
4.3.2 Assignment of Values in R and Computations Using Vectors and Matrices
4.3.3 Computations in Vectors and Simple Graphics
4.3.4 Use of Factors in R Programming
4.3.6 x as Vectors and Matrices in Statistics
4.3.7 Some Special Functions that Create Vectors
4.3.8 Arrays and Matrices
4.3.9 Use of the Dimension Function dim() in R
4.3.10 Use of the Matrix Function matrix() In R
4.3.11 Some Useful Functions Operating on Matrices in R: Colnames, Rownames, and t (for transpose)
4.3.12 NA ``Not Available´´ for Missing Values in Data sets
4.3.13 Special Functions That Create Vectors
4.4 Using R in Data Analysis in Financial Engineering
4.4.1 Entering Data at the R Command Prompt
4.4.1.1 Creating a Data Frame for R Computation Using the EXCEL Spreadsheet (on a Windows Platform)
4.4.1.2 Obtaining a Data Frame from a Text File
4.4.1.3 Data Entry and Analysis Using the Function data.entry()
4.4.1.4 Data Entry Using Several Available R Functions
4.4.1.5 Data Entry and Analysis Using the Function scan()
4.4.1.6 Data Entry and Analysis Using the Function Source()
4.4.1.7 Data Entry and Analysis Using the Spreadsheet Interface in R
4.4.1.8 Financial Mathematics Using R: The CRAN Package FinancialMath
4.4.2 The Function list() and the Construction of data.frame() in R
4.4.3 Stock Market Risk Analysis: ES (Expected Shortfall) in the Black-Scholes Model
4.5 Univariate, Bivariate, and Multivariate Data Analysis
4.5.1 Univariate Data Analysis
4.5.2 Bivariate and Multivariate Data Analysis
5: Assets Allocation Using R
5.1 Risk Aversion and the Assets Allocation Process
5.2 Classical Assets Allocation Approaches
5.2.1 Going Beyond α and β
5.2.3 The Mortality Model
5.2.4 Sensitivity Analysis
5.2.4.1 The Elasticity of Intertemporal Substitution (EOIS)
5.3 Allocation with Time Varying Risk Aversion
5.3.1.1 Example of a Risk-Averse/Neutral/Loving Investor
5.3.1.2 Expected Utility Theory
5.3.1.3 Utility Functions
5.4 Variable Risk Preference Bias
5.4.1 Time-Varying Risk Aversion
5.4.1.1 The Rationale Behind Time-Varying Risk Aversion
5.4.1.2 Risk Tolerance for Time-Varying Risk Aversion
5.5 A Unified Approach for Time Varying Risk Aversion
5.6 Assets Allocation Worked Examples
5.6.1 Worked Example 1: Assets Allocation Using R
5.6.2 Worked Example 2: Assets Allocation Using R, from CRAN
5.6.3 Worked Example 3: The Black–Litterman Asset
6: Financial Risk Modeling and Portfolio Optimization Using R
6.1 Introduction to the Optimization Process
6.1.1 Classical Optimization Approach in Mathematics
6.1.1.1 Global and Local Optimal Values
6.1.1.2 Graphical Illustrations of Global and Local Optimal Value
6.1.2 Locating Functional Maxima and Minima
6.2 Optimization Methodologies in Probabilistic Calculus for Financial Engineering
6.2.1 The Evolutionary Algorithms (EA)
6.2.2 The Differential Evolution (DE) Algorithm
6.3 Financial Risk Modeling and Portfolio Optimization
6.3.1 An Example of a Typical Professional Organization in Wealth Management
6.3.1.1 LPL (Linsco Private Ledger) Financial
6.4 Portfolio Optimization Using R
6.4.1 Portfolio Optimization by Differential Evolution (DE) Using R
6.4.2 Portfolio Optimization by Special Numerical Methods
6.4.3 Portfolio Optimization by the Black-Litterman Approach Using R
6.4.3.1 A Worked Example Portfolio Optimization by the Black-Litterman Approach Using R
6.4.4 More Worked Examples of Portfolio Optimization Using R
6.4.4.1 Worked Examples of Portfolio Optimization - No. 1 Portfolio Optimization by PerformanceAnalytics in CRAN
6.4.4.2 Worked Example for Portfolio Optimization - No. 2 Portfolio Optimization using the R code DEoptim
6.4.4.3 Worked Example for Portfolio Optimization - No. 3 Portfolio Optimization Using the R Code PortfolioAnalytics in CRAN
6.4.4.4 Worked Example for Portfolio Optimization - Portfolio Optimization by AssetsM in CRAN
6.4.4.5 Worked Examples from Pfaff
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Applied Probabilistic Calculus for Financial Engineering
：An Introduction Using R
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