概率论及其在投资、保险、工程中的应用 英文版2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

概率论及其在投资、保险、工程中的应用 英文版PDF格式电子书版下载

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1 Introduction1

1．1 What Is Probability?1

1．2 How Is Uncertainty Quantified?2

1．3 Probability in Engineering and the Sciences5

1．4 What Is Actuarial Science?6

1．5 What Is Financial Engineering?9

1．6 Interpretations of Probability11

1．7 Probability Modeling in Practice13

1．8 Outline of This Book14

1．9 Chapter Summary15

1．10 Further Reading16

1．11 Exercises17

2 A Survey of some Basic concepts Through Examples19

2．1 Payoff in a Simple Game19

2．2 Choosing Between Payoffs25

2．3 Future Lifetimes36

2．4 Simple and Compound Growth42

2．5 Chapter Summary49

2．6 Exercises51

3 Classical Probability57

3．1 The Formal Language of Classical Probability58

3．2 Conditional Probability64

3．3 The Law of Total Probability68

3．4 Bayes’Theorem72

3．5 Chapter Summary75

3．6 Exercises76

3．7 Appendix on Sets,Combinatorics,and Basic Probability Rules85

4 Random Variables and Probability Distributions91

4．1 Definitions and Basic Properties91

4．1．1 What Is Random Variable?91

4．1．2 What Is a Probability Distribution?92

4．1．3 Types of Distributions94

4．1．4 Probability Mass Functions97

4．1．5 Probability Density Functions97

4．1．6 Mixed Distributions100

4．1．7 Equality and Equivalence of Random Variables102

4．1．8 Random Vectors and Bivariate Distributions104

4．1．9 Dependence and Independence of Random Variables113

4．1．10 The Law of Total Probability and Bayes’Theorem(Distributional Forms)119

4．1．11 Arithmetic Operations on Random Variables124

4．1．12 The Difference Between Sums and Mixtures125

4．1．13 Exercises126

4．2 Statistical Measures of Expectation,Variation,and Risk130

4．2．1 Expectation130

4．2．2 Deviation from Expectation143

4．2．3 Higher Moments149

4．2．4 Exercises153

4．3 Alternative Ways of specifying Probability Distributions155

4．3．1 Moment and Cumulant Generating Functions155

4．3．2 Survival and Hazard Functions167

4．3．3 Exercises170

4．4 Chapter Summary173

4．5 Additional Exercises177

4．6 Appendix on Generalized Density Functions(Optional)178

5 Special Discrete Distributions186

5．1 The Binomial Distribution187

5．2 The Poisson Distribution195

5．3 The Negative Binomial Distribution200

5．4 The Geometric Distribution206

5．5 Exercises209

6．1．1 The Exponential Distribution221

6．1 Special Continuous Distributions for Modeling Uncertain Sizes221

6 Special Continuous Distributions221

6．1．2 The Gamma Distribution226

6．1．3 The Pareto Distribution233

6．2 Special Continuous Distributions for Modeling Lifetimes235

6．2．1 The Weibull Distribution235

6．2．2 The DeMoivre Distribution241

6．3 Other Special Distributions245

6．3．1 The Normal Distribution245

6．3．2 The Lognormal Distribution256

6．3．3 The Beta Distribution260

6．4 Exercises265

7 Transformation of Random Variables280

7．1 Determining the Distribution of a Transformed Random Variable281

7．2 Expectation of a Transformed Random Variable289

7．3 Insurance Contracts with Caps,Deductibles,and Coinsurance(Optional)297

7．4 Life Insurance and Annuity Contracts(Optional)303

7．5 Reliability of Systems with Multiple Components or Processes(Optional)311

7．6 Trigonometric Transformations(Optional)317

7．7 Exercises319

8 Sums and Products of Random Variables325

8．1 Techniques for Calculating the Distribution of a Sum325

8．1．1 Using The Joint Density326

8．1．2 Using The Law of Total Probability331

8．1．3 Convolutions336

8．2 Distributions of Products and Quotients337

8．3 Expectations of Sums and Products339

8．3．1 Formulas for The Expectation of a Sum or Product339

8．3．2 The Cauchy-Schwarz Inequality340

8．3．3 Covariance and Correlation341

8．4 The Law of Large Numbers345

8．4．1 Motivating Example：Premium Determination in Insurance346

8．4．2 Statement and Proof of the Law349

8．4．3 Some Misconceptions Surrounding the Law of Large Numbers351

8．5 The Central Limit Theorem352

8．6 Normal Power Approximations(Optional)354

8．7 Exercises356

9 Mixtures and Compound Distributions363

9．1 Definitions and Basic Properties363

9．2 Some Important Examples of Mixtures Arising in Insurance366

9．3 Mean and Variance of a Mixture373

9．4 Moment Generating Function of a Mixture378

9．5 Compound Distributions379

9．5．1 General Formulas380

9．5．2 Special Compound Distributions382

9．6 Exercises384

10 The Markowitz Investment Portfolio Selection Model396

10．1 Portfolios of Two Securities397

10．2 Portfolios of Two Risky Securities and a Risk-Free Asset403

10．3 Portfolio Selection with Many Securities409

10．4 The Capital Asset Pricing Model411

10．5 Further Reading414

10．6 Exercises415

Appendixes421

A The Gamma Function421

B The Incomplete Gamma Function423

C The Beta Function428

D The Incomplete Beta Function429

E The Standard Normal Distribution430

F Mathematica Commands for Generating the Graphs of Special Distributions432

G Elementary Financial Mathematics434

Answers to Selected Exercises437

Index441