精算模型 寿险和年金 英文版PDF|Epub|txt|kindle电子书版本网盘下载

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1 Interest and Annuity-Certain1

1.1 Introduction1

1.2 Interest1

1.2.1 Simple Interest1

1.2.2 Compound Interest2

1.2.3 Interest Convertible m-thly3

1.2.4 Force of Interest4

1.2.5 Relationship among Interest Rates5

1.2.6 The Accumulation Factor5

1.2.7 The Discount Factor6

1.3 Annuities-Certain6

1.3.1 Annual Annuities-Certain6

1.3.2 Continuous Annuities-Certain10

1.3.3 m-thly Annuities-Certain12

1.3.4 Accumulated Values of Annuities-Certain at Time n14

1.4 Summary14

1.5 Exercise17

2 Individual Future Lifetime21

2.1 Introduction21

2.2 A Newborn's Future Lifetime X21

2.3 Future Lifetime of(x)26

2.3.1 Relationship Between Probability Functions of X and T(x)28

2.3.2 Curtate-Future-Lifetime of(x)32

2.3.3 Conditional Average Death Time33

2.3.4 Central Force of Mortality34

2.4 Life Table34

2.4.1 Aggregate Life Table35

2.4.2 Select-and-Ultimate Life Table42

2.5 Summary49

2.6 Exercise52

3 Life Insurance59

3.1 Introduction59

3.2 Continuous Life Insurance59

3.2.1 Level Life Insurance60

3.2.2 A General Continuous Life Insurance65

3.3 Discrete Life Insurance68

3.3.1 Level Life Insurance68

3.3.2 A General Discrete Life Insurance71

3.3.3 Commutation Functions73

3.4 m-thly Life Insurance77

3.5 Endowment Insurance80

3.6 Summary82

3.7 Exercise85

4 Life Annuities93

4.1 Introduction93

4.2 Continuous Life Annuities94

4.2.1 Level Life Annuities94

4.2.2 Varying Continuous Life Annuities99

4.3 Annual Life Annuities101

4.3.1 Level Annual Life Annuities101

4.3.2 Varying Annual Life Annuities106

4.3.3 Commutation Functions107

4.4 Special Life Annuities112

4.4.1 m-thly Life Annuities112

4.4.2 n-Year-Certain-and-Life Annuities118

4.4.3 Apportionable Annuities-Due119

4.4.4 Complete Annuities-Immediate120

4.5 Summary121

4.6 Exercise127

5 Insurance Premiums135

5.1 Introduction135

5.2 Insurance Pricing Principles135

5.2.1 The Three Pricing Principles137

5.2.2 Single Benefit Premiums140

5.3 Benefit Premiums141

5.3.1 Fully Continuous Benefit Premiums142

5.3.2 Fully Discrete Benefit Premiums144

5.3.3 m-thly Benefit Premiums148

5.3.4 Apportionable Benefit Premiums150

5.4 Gross Insurance Premiums152

5.4.1 Classification of Expenses152

5.4.2 Gross Premiums Under the Equivalence Principle153

5.5 Summary155

5.6 Exercises160

6 Insurance Reserves173

6.1 Introduction173

6.2 Insurance Reserve Principles173

6.2.1 The Prcspective Loss Random Variable174

6.2.2 The Three Common Principles175

6.3 Insurance Benefit Reserves177

6.3.1 Benefit Reserves for Fully Continuous Life Insurance178

6.3.2 Benefit Reserves for Fully Discrete Life Insurance183

6.3.3 Benefit Reserves with the Retrospective Method187

6.3.4 Recursive Formula between Discrete Benefit Reserves190

6.4 Benefit Reserves for Special Life Insurance197

6.4.1 Benefit Reserves for m-thly Life Insurance197

6.4.2 Benefit Reserves for Mixed Life Insurance199

6.4.3 Benefit Reserves with Apportionable Premiums200

6.4.4 Gross Insurance Reserves202

6.5 Summary203

6.6 Excercise207

7 Joint-Life Functions223

7.1 Introduction223

7.2 Joint Distributions of Future Lifetimes223

7.2.1 The Joint-Life Status226

7.2.2 Last-Survivor Status(？)230

7.3 Relationship among T(x),T(y),Txy,and T？233

7.4 Contingent Probabilities236

7.5 Dependent Models240

7.5.1 Common Shock Model240

7.5.2 Frank's Copula243

7.6 Life Insurance on Two Individuals245

7.6.1 Life Insurance on(xy) and (？)245

7.6.2 Contingent Life Insurance249

7.7 Life Annuities on Two Individuals250

7.7.1 Life Annuities on(xy) and (？)250

7.7.2 Reversionary Annuities252

7.8 Summary254

7.9 Exercise257

8 Multiple-Decrement Model271

8.1 Introduction271

8.2 A Double-Decrement Model271

8.2.1 Future Lifetimes of Two Risks271

8.2.2 Probabilities of Decrement276

8.3 A General m-Decrement Model282

8.3.1 Probabilities of Decrement282

8.3.2 Central Rates from a Multiple-Decrement Table287

8.3.3 Constructing a Multiple-Decrement Table289

8.4 Discretionary Life Insurance294

8.4.1 Benefit Premiums for Discretionary Life Insurance296

8.4.2 Benefit Reserves for Discretionary Life Insurance297

8.4.3 Asset Share298

8.5 Summary302

8.6 Exercise305

Appendix 1 Standard Normal Table321

Appendix 2A Illustrative Life Table with i=0.06322

Appendix 2B Illustrative Service Table with i=0.06326

Appendix 2C Interest Rate Function at i=0.06327

Appendix 3 Probability Theorem and Random Variables328

Appendix 4 Interest Rate and Annuity-Certain331

Bibliography333

Symbol Index334

Index339