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El. knyga: Extreme Financial Risks and Asset Allocation [World Scientific e-book]

(Fondation Maison Des Sciences De L'homme, France), (Em Lyon Business Sch, France)
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Extreme Financial Risks and Asset AllocationDidesnis paveikslėlis
Kitos knygos pagal šią temą:
World Scientific e-booksMore info about World Scientific e-books
Partnerių interneto svetainė: http://www.worldscientific.com/worldscibooks/10.1142/P907#t=toc
Each financial crisis calls for — by its novelty and the mechanisms it shares with preceding crises — appropriate means to analyze financial risks. In Extreme Financial Risks and Asset Allocation, the authors present in an accessible and timely manner the concepts, methods, and techniques that are essential for an understanding of these risks in an environment where asset prices are subject to sudden, rough, and unpredictable changes. These phenomena, mathematically known as “jumps”, play an important role in practice. Their quantitative treatment is generally tricky and is sparsely tackled in similar books. One of the main appeals of this book lies in its approachable and concise presentation of the ad hoc mathematical tools without sacrificing the necessary rigor and precision.This book contains theories and methods which are usually found in highly technical mathematics books or in scattered, often very recent, research articles. It is a remarkable pedagogical work that makes these difficult results accessible to a large readership. Researchers, Masters and PhD students, and financial engineers alike will find this book highly useful.
Foreword v
Preface ix
1 Introduction
1(8)
2 Market Framework
9(22)
2.1 Studied Quantities
10(12)
2.1.1 Financial Assets
10(2)
2.1.2 Portfolios
12(7)
2.1.3 Distribution Parameters
19(3)
2.2 The Question of Time
22(9)
2.2.1 Choosing the Measure of Time
22(3)
2.2.2 Choosing the Scale of Time
25(6)
3 Statistical Description of Markets
31(22)
3.1 Construction of a Representation
32(2)
3.1.1 Role of the Statistical Description
32(1)
3.1.2 Continuous or Discontinuous Representations
32(2)
3.2 Normality Tests
34(5)
3.2.1 The Pearson---Fisher Coefficients
35(2)
3.2.2 Kolmogorov Test
37(2)
3.3 Discontinuity Test
39(6)
3.3.1 Definition of Estimators
39(2)
3.3.2 Confidence Intervals
41(4)
3.4 Continuity Test
45(2)
3.4.1 Definition of the Estimators
45(1)
3.4.2 Confidence Interval
46(1)
3.5 Testing the Finiteness of the Activity
47(6)
3.5.1 Construction of the Tests
48(2)
3.5.2 Illustration
50(3)
4 Levy Processes
53(24)
4.1 Definitions and Construction
54(6)
4.1.1 The Characteristic Exponent
54(1)
4.1.2 Infinitely Divisible Distributions
54(1)
4.1.3 A Construction with Poisson Processes
55(5)
4.2 The Levy--Khintchine Formula
60(7)
4.2.1 Form of the Characteristic Exponent
60(2)
4.2.2 The Levy Measure
62(5)
4.3 The Moments of Levy Processes of Finite Variation
67(10)
4.3.1 Existence of the Moments
68(1)
4.3.2 Calculating the Moments
69(8)
5 Stable Distributions and Processes
77(28)
5.1 Definitions and Properties
78(22)
5.1.1 Definitions
78(3)
5.1.2 Characteristic Function and Levy Measure
81(9)
5.1.3 Some Special Cases of Stable Distributions
90(4)
5.1.4 Simulating Paths of Stable Processes
94(6)
5.2 Stable Financial Models
100(5)
5.2.1 With Pure Stable Distributions
100(1)
5.2.2 With Tempered Stable Distributions
101(4)
6 Laplace Distributions and Processes
105(42)
6.1 The First Laplace Distribution
106(23)
6.1.1 The Intuitive Approach
106(2)
6.1.2 Representations of the Laplace Distribution
108(9)
6.1.3 Laplace Motion
117(12)
6.2 The Asymmetrization of the Laplace Distribution
129(7)
6.2.1 Construction of the Asymmetrization
129(5)
6.2.2 Laplace Processes
134(2)
6.3 The Laplace Distribution as the Limit of Hyperbolic Distributions
136(11)
6.3.1 Motivation for Hyperbolic Distributions
138(1)
6.3.2 Construction of Hyperbolic Distributions
139(4)
6.3.3 Hyperbolic Distributions as Mixture Distributions
143(4)
7 The Time Change Framework
147(34)
7.1 Time Changes
148(7)
7.1.1 Historical Survey
148(1)
7.1.2 A First Modeling Example
149(6)
7.2 Subordinated Brownian Motions
155(18)
7.2.1 The Mechanics of Subordination
155(3)
7.2.2 Construction of a Time Change
158(7)
7.2.3 Brownian Motion in Gamma Time
165(8)
7.3 Time-Changed Laplace Process
173(8)
7.3.1 Mean-Reverting Clock
174(4)
7.3.2 The Laplace Process in ICIR Time
178(3)
8 Tail Distributions
181(46)
8.1 Largest Values Approach
181(13)
8.1.1 The Laws of Maxima
182(8)
8.1.2 The Maxima of Levy Processes
190(4)
8.2 Threshold Approach
194(8)
8.2.1 The Law of Threshold Exceedances
194(4)
8.2.2 Linearity of Means beyond Thresholds
198(4)
8.3 Statistical Phenomenon Approach
202(18)
8.3.1 Concentration of Results
202(14)
8.3.2 Hierarchy of Large Values
216(4)
8.4 Estimation of the Shape Parameter
220(7)
8.4.1 A New Algorithm
221(3)
8.4.2 Examples of Results
224(3)
9 Risk Budgets
227(26)
9.1 Risk Measures
228(14)
9.1.1 Main Issues
228(2)
9.1.2 Definition of the Main Risk Measures
230(3)
9.1.3 VaR, TCE, and the Laws of Maximum
233(2)
9.1.4 Notion of Model Risk
235(7)
9.2 Computation of Risk Budgets
242(11)
9.2.1 Numerical Method
242(5)
9.2.2 Semi-Heavy Distribution Tails
247(3)
9.2.3 Heavy Distribution Tails
250(3)
10 The Psychology of Risk
253(22)
10.1 Basic Principles of the Psychology of Risk
254(2)
10.1.1 The Notion of Psychological Value
254(1)
10.1.2 The Notion of Certainty Equivalent
255(1)
10.2 The Measurement of Risk Aversion
256(11)
10.2.1 Definitions of the Risk Premium
256(2)
10.2.2 Decomposition of the Risk Premium
258(6)
10.2.3 Illustration
264(3)
10.3 Typology of Risk Aversion
267(8)
10.3.1 Attitude with Respect to Financial Risk
268(1)
10.3.2 The Family of HARA Functions
269(6)
11 Monoperiodic Portfolio Choice
275(28)
11.1 The Optimization Program
277(2)
11.2 Optimizing with Two Moments
279(5)
11.2.1 One Risky Asset
280(2)
11.2.2 Several Risky Assets
282(2)
11.3 Optimizing with Three Moments
284(5)
11.3.1 One Risky Asset
284(4)
11.3.2 Several Risky Assets
288(1)
11.4 Optimizing with Four Moments
289(5)
11.4.1 One Risky Asset
289(3)
11.4.2 Several Risky Assets
292(2)
11.5 Other Problems
294(9)
11.5.1 Giving up Comoments
294(2)
11.5.2 Perturbative Approach and Normalized Moments
296(1)
Appendix: Dealing with Uncertainty
297(6)
12 Dynamic Portfolio Choice
303(28)
12.1 The Optimization Program
304(11)
12.1.1 The Objective Function
304(4)
12.1.2 Modeling Stock Fluctuations
308(7)
12.2 Classic Approach
315(4)
12.3 Optimization in the Presence of Jumps
319(12)
12.3.1 Presentation of the Model
319(3)
12.3.2 Illustration
322(3)
Appendix: Dealing with Uncertainty
325(6)
13 Conclusion
331(2)
Appendix A Concentration vs Diversification 333(8)
Bibliography 341(8)
Index 349
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