发帖
雷达卡
Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures (Frank J. Fabozzi Series) (Hardcover)
by Svetlozar T. Rachev (Author), Stoyan V. Stoyanov (Author), Frank J. Fabozzi (Author)
This groundbreaking book extends traditional approaches of risk measurement and portfolio optimization by combining distributional models with risk or performance measures into one framework. Throughout these pages, the expert authors explain the fundamentals of probability metrics, outline new approaches to portfolio optimization, and discuss a variety of essential risk measures. Using numerous examples, they illustrate a range of applications to optimal portfolio choice and risk theory, as well as applications to the area of computational finance that may be useful to financial engineers.
From the Inside Flap
S ince the 1990s, significant progress has been made in developing the concept of a risk measure from both a theoretical and a practical viewpoint. This notion has evolved into a materially different form from the original idea behind traditional mean-variance analysis. As a consequence, the distinction between risk and uncertainty, which translates into a distinction between a risk measure and a dispersion measure, offers a new way of looking at the problem of optimal portfolio selection.
In Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization, the authors assert that the ideas behind the concept of probability metrics can be borrowed and applied in the field of asset management in order to construct an ideal risk measure which would be "ideal" for a given optimal portfolio selection problem. They provide a basic introduction to the theory of probability metrics and the problem of optimal portfolio selection considered in the general context of risk and reward measures.
Generally, the theory of probability metrics studies the problem of measuring distances between random quantities. There are no limitations in the theory of probability metrics concerning the nature of the random quantities, which makes its methods fundamental and appealing. Actually, it is more appropriate to refer to the random quantities as random elements: they can be random variables, random vectors, random functions, or random elements of general spaces. In the context of financial applications, we can study the distance between two random stocks prices, or between vectors of financial variables building portfolios, or between entire yield curves that are much more complicated objects. The methods of the theory remain the same, no matter the nature of the random elements.
Using numerous illustrative examples, this book shows how probability metrics can be applied to a range of areas in finance, including: stochastic dominance orders, the construction of risk and dispersion measures, problems involving average value-at-risk and spectral risk measures in particular, reward-risk analysis, generalizing mean-variance analysis, benchmark tracking, and the construction of performance measures. For each chapter where more technical knowledge is necessary, an appendix is included.
198245.pdf
(3.83 MB, 需要: 26 个论坛币)
Contents
Preface xiii
Acknowledgments xv
About the Authors xvii
CHAPTER 1
Concepts of Probability 1
1.1 Introduction 1
1.2 Basic Concepts 2
1.3 Discrete Probability Distributions 2
1.4 Continuous Probability Distributions 5
1.5 Statistical Moments and Quantiles 13
1.6 Joint Probability Distributions 17
1.7 Probabilistic Inequalities 30
1.8 Summary 32
CHAPTER 2
Optimization 35
2.1 Introduction 35
2.2 Unconstrained Optimization 36
2.3 Constrained Optimization 48
2.4 Summary 58
CHAPTER 3
Probability Metrics 61
3.1 Introduction 61
3.2 Measuring Distances: The Discrete Case 62
3.3 Primary, Simple, and Compound Metrics 72
3.4 Summary 90
3.5 Technical Appendix 90
CHAPTER 4
Ideal Probability Metrics 103
4.1 Introduction 103
4.2 The Classical Central Limit Theorem 105
4.3 The Generalized Central Limit Theorem 120
4.4 Construction of Ideal Probability Metrics 124
4.5 Summary 131
4.6 Technical Appendix 131
CHAPTER 5
Choice under Uncertainty 139
5.1 Introduction 139
5.2 Expected Utility Theory 141
5.3 Stochastic Dominance 147
5.4 Probability Metrics and Stochastic Dominance 157
5.5 Summary 161
5.6 Technical Appendix 161
CHAPTER 6
Risk and Uncertainty 171
6.1 Introduction 171
6.2 Measures of Dispersion 174
6.3 Probability Metrics and Dispersion Measures 180
6.4 Measures of Risk 181
6.5 Risk Measures and Dispersion Measures 198
6.6 Risk Measures and Stochastic Orders 199
6.7 Summary 200
6.8 Technical Appendix 201
CHAPTER 7
Average Value-at-Risk 207
7.1 Introduction 207
7.2 Average Value-at-Risk 208
7.3 AVaR Estimation from a Sample 214
7.4 Computing Portfolio AVaR in Practice 216
7.5 Backtesting of AVaR 220
Contents xi
7.6 Spectral Risk Measures 222
7.7 Risk Measures and Probability Metrics 224
7.8 Summary 227
7.9 Technical Appendix 227
CHAPTER 8
Optimal Portfolios 245
8.1 Introduction 245
8.2 Mean-Variance Analysis 247
8.2.4 Adding a Risk-Free Asset 256
8.3 Mean-Risk Analysis 258
8.4 Summary 274
8.5 Technical Appendix 274
CHAPTER 9
Benchmark Tracking Problems 287
9.1 Introduction 287
9.2 The Tracking Error Problem 288
9.3 Relation to Probability Metrics 292
9.4 Examples of r.d. Metrics 296
9.5 Numerical Example 300
9.6 Summary 304
9.7 Technical Appendix 304
CHAPTER 10
Performance Measures 317
10.1 Introduction 317
10.2 Reward-to-Risk Ratios 318
10.3 Reward-to-Variability Ratios 333
10.4 Summary 343
10.5 Technical Appendix 343
Index 361
提升卡
置顶卡
沉默卡
变色卡
抢沙发
千斤顶
显身卡
京公网安备 11010802022788号
