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E-grāmata: Financial and Actuarial Statistics: An Introduction, Second Edition

(Pennsylvania State University, University Park, USA), (University of Akron, Ohio, USA)
  • Formāts: 392 pages
  • Izdošanas datums: 12-Nov-2013
  • Izdevniecība: Chapman & Hall/CRC
  • Valoda: eng
  • ISBN-13: 9781135541040
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  • Formāts: 392 pages
  • Izdošanas datums: 12-Nov-2013
  • Izdevniecība: Chapman & Hall/CRC
  • Valoda: eng
  • ISBN-13: 9781135541040
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"Preface Financial and actuarial modeling is an ever-changing field with an increased reliance on statistical techniques. This is seen in the changing of competency exams, especially at the upper levels, where topics include more statistical concepts andtechniques. In the years since the first edition was published statistical techniques such as reliability measurement, simulation, regression, and Markov chain modeling have become more prominent. This influx in statistics has put an increased pressure on students to secure both strong mathematical and statistical backgrounds and the knowledge of statistical techniques in order to have successful careers. As in the first edition, this text approaches financial and actuarial modeling from a statistical point of view. The goal of this text is twofold. The first is to provide students and practitioners a source for required mathematical and statistical background. The second is to advance the application and theory of statistics in financial and actuarial modeling. This text presents a unified approach to both financial and actuarial modeling through the utilization of general status structures. Future timedependent financial actions are defined in terms of a status structure that may be either deterministic or stochastic. Deterministic status structures lead to classical interest and annuity models, investment pricing models, and aggregate claim models. Stochastic status structures are used to develop financial and actuarial models, such as surplus models,life insurance, and life annuity models. This edition is updated with the addition of nomenclature and notations standard to the actuarial field"--

"Presenting a unique interface between statistics and financial/actuarial topics, this second edition provides a solid background for students preparing for a career in actuarial science. It explores novel research areas and adds more problems, along with a new solutions section. This edition also includes a new chapter on Markov chain theory with applications to mortality and multiple decrement mortality table modeling, a presentation of model checking diagnostics that covers diagnostics for mortality tables, and an expanded discussion on option pricing with examples"--

Presenting a unique interface between statistics and financial/actuarial topics, this second edition provides a solid background for students preparing for a career in actuarial science. It explores novel research areas and adds more problems, along with a new solutions section. This edition also includes a new chapter on Markov chain theory with applications to mortality and multiple decrement mortality table modeling, a presentation of model checking diagnostics that covers diagnostics for mortality tables, and an expanded discussion on option pricing with examples.

Preface ix
1 Statistical Concepts 1(40)
1.1 Probability
1(6)
1.2 Random Variables
7(7)
1.2.1 Discrete Random Variables
8(2)
1.2.2 Continuous Random Variables
10(3)
1.2.3 Mixed Random Variables
13(1)
1.3 Expectations
14(6)
1.4 Moment Generating Function
20(2)
1.5 Survival Functions
22(3)
1.6 Nonnegative Random Variables
25(4)
1.6.1 Pareto Distribution
25(1)
1.6.2 Lognormal Distribution
26(1)
1.6.3 Weibull Distribution
26(1)
1.6.4 Gompertz Distribution
27(1)
1.6.5 Makeham Distribution
28(1)
1.7 Conditional Distributions
29(2)
1.8 Joint Distributions'
31(5)
Problems
36(2)
Excel Problems
38(1)
Solutions
38(3)
2 Statistical Techniques 41(52)
2.1 Sampling Distributions and Estimation
41(8)
2.1.1 Point Estimation
42(2)
2.1.2 Confidence Intervals
44(1)
2.1.3 Percentiles and Prediction Intervals
45(1)
2.1.4 Confidence and Prediction Sets
46(3)
2.2 Sums of Independent Variables
49(5)
2.3 Order Statistics and Empirical Prediction Intervals
54(3)
2.4 Approximating Aggregate Distributions
57(8)
2.4.1 Central Limit Theorem
57(4)
2.4.2 Haldane Type A Approximation
61(1)
2.4.3 Saddlepoint Approximation
62(3)
2.5 Compound Aggregate Variables
65(5)
2.5.1 Expectations of Compound Aggregate Variables
65(1)
2.5.2 Limiting Distributions for Compound Aggregate Variables
66(4)
2.6 Regression Modeling
70(5)
2.6.1 Least Squares Estimation
71(3)
2.6.2 Regression Model-Based Inference
74(1)
2.7 Autoregressive Systems
75(3)
2.8 Model Diagnostics
78(9)
2.8.1 Probability Plotting
79(4)
2.8.2 Generalized Least Squares Diagnostic
83(1)
2.8.3 Interval Data Diagnostic
84(3)
Problems
87(1)
Excel Problems
88(2)
Solutions
90(3)
3 Financial Computational Models 93(30)
3.1 Fixed Financial Rate Models
94(7)
3.1.1 Financial Rate-Based Calculations
94(5)
3.1.2 General Period Discrete Rate Models
99(1)
3.1.3 Continuous-Rate Models
100(1)
3.2 Fixed-Rate Annuities
101(5)
3.2.1 Discrete Annuity Models
101(3)
3.2.2 Continuous Annuity Models
104(2)
3.3 Stochastic Rate Models
106(11)
3.3.1 Discrete Stochastic Rate Model
106(6)
3.3.2 Continuous Stochastic Rate Models
112(2)
3.3.3 Discrete Stochastic Annuity Models
114(2)
3.3.4 Continuous Stochastic Annuity Models
116(1)
Problems
117(2)
Excel Problems
119(1)
Solutions
120(3)
4 Deterministic Status Models 123(40)
4.1 Basic Loss Model
123(5)
4.1.1 Deterministic Loss Models
124(2)
4.1.2 Stochastic Rate Models
126(2)
4.2 Stochastic Loss Criterion
128(3)
4.2.1 Risk Criteria
129(1)
4.2.2 Percentile Criteria
130(1)
4.3 Single-Risk Models
131(9)
4.3.1 Insurance Pricing
131(4)
4.3.2 Investment Pricing
135(1)
4.3.3 Options Pricing
136(3)
4.3.4 Option Pricing Diagnostics
139(1)
4.4 Collective Aggregate Models
140(8)
4.4.1 Fixed Number of Variables
141(2)
4.4.2 Stochastic Number of Variables
143(2)
4.4.3 Aggregate Stop-Loss Reinsurance and Dividends
145(3)
4.5 Stochastic Surplus Model
148(7)
4.5.1 Discrete Surplus Model
148(4)
4.5.2 Continuous Surplus Model
152(3)
Problems
155(3)
Excel Problems
158(1)
Solutions
159(4)
5 Future Lifetime Random Variables and Life Tables 163(40)
5.1 Continuous Future Lifetime
164(3)
5.2 Discrete Future Lifetime
167(2)
5.3 Force of Mortality
169(6)
5.4 Fractional Ages
175(2)
5.5 Select Future Lifetimes
177(2)
5.6 Survivorship Groups
179(3)
5.7 Life Models and Life Tables
182(3)
5.8 Life Table Confidence Sets and Prediction Intervals
185(2)
5.9 Life Models and Life Table Parameters
187(7)
5.9.1 Population Parameters
188(3)
5.9.2 Aggregate Parameters
191(2)
5.9.3 Fractional Age Adjustments
193(1)
5.10 Select and Ultimate Life Tables
194(4)
Problems
198(2)
Excel Problems
200(1)
Solutions
200(3)
6 Stochastic Status Models 203(54)
6.1 Stochastic Present Value Functions
204(1)
6.2 Risk Evaluations
205(3)
6.2.1 Continuous-Risk Calculations
205(1)
6.2.2 Discrete Risk Calculations
206(1)
6.2.3 Mixed Risk Calculations
207(1)
6.3 Percentile Evaluations
208(2)
6.4 Life Insurance
210(5)
6.4.1 Types of Unit Benefit Life Insurance
212(3)
6.5 Life Annuities
215(8)
6.5.1 Types of Unit Payment Life Annuities
217(3)
6.5.2 Apportionable Annuities
220(3)
6.6 Relating Risk Calculations
223(4)
6.6.1 Relations among Insurance Expectations
223(2)
6.6.2 Relations among Insurance and Annuity Expectations
225(1)
6.6.3 Relations among Annuity Expectations
226(1)
6.7 Actuarial Life Tables
227(3)
6.8 Loss Models and Insurance Premiums
230(7)
6.8.1 Unit Benefit Premium Notation
232(3)
6.8.2 Variance of the Loss Function
235(2)
6.9 Reserves
237(7)
6.9.1 Unit Benefit Reserves Notations
240(1)
6.9.2 Relations among Reserve Calculations
241(2)
6.9.3 Survivorship Group Approach to Reserve Calculations
243(1)
6.10 General Time Period Models
244(5)
6.10.1 General Period Expectation
245(1)
6.10.2 Relations among General Period Expectations
246(3)
6.11 Expense Models and Computations
249(3)
Problems
252(2)
Excel Problems
254(1)
Solutions
254(3)
7 Advanced Stochastic Status Models 257(38)
7.1 Multiple Future Lifetimes
257(7)
7.1.1 Joint Life Status
258(2)
7.1.2 Last Survivor Status
260(3)
7.1.3 General Contingent Status
263(1)
7.2 Multiple-Decrement Models
264(16)
7.2.1 Continuous Multiple Decrements
264(2)
7.2.2 Forces of Decrement
266(2)
7.2.3 Discrete Multiple Decrements
268(1)
7.2.4 Single-Decrement Probabilities
269(2)
7.2.5 Uniformly Distributed Single-Decrement Rates
271(2)
7.2.6 Single-Decrement Probability Bounds
273(2)
7.2.7 Multiple-Decrement Life Tables
275(3)
7.2.8 Single-Decrement Life Tables
278(1)
7.2.9 Multiple-Decrement Computations
279(1)
7.3 Pension Plans
280(10)
7.3.1 Multiple-Decrement Benefits
281(4)
7.3.2 Pension Contributions
285(2)
7.3.3 Future Salary-Based Benefits and Contributions
287(1)
7.3.4 Yearly Based Retirement Benefits
288(2)
Problems
290(1)
Excel Problems
291(1)
Solutions
292(3)
8 Markov Chain Methods 295(28)
8.1 Introduction to Markov Chains
296(1)
8.2 Nonhomogeneous Stochastic Status Chains
297(10)
8.2.1 Single-Decrement Chains
298(1)
8.2.2 Actuarial Chains
299(1)
8.2.3 Multiple-Decrement Chains
300(3)
8.2.4 Multirisk Strata Chains
303(4)
8.3 Homogeneous Stochastic Status Chains
307(5)
8.3.1 Expected Curtate Future Lifetime
309(1)
8.3.2 Actuarial Chains
310(2)
8.4 Survivorship Chains
312(4)
8.4.1 Single-Decrement Models
313(1)
8.4.2 Multiple-Decrement Models
314(1)
8.4.3 Multirisk Strata Models
315(1)
Problems
316(1)
Excel Problems
317(3)
Solutions
320(3)
9 Scenario and Simulation Testing 323(30)
9.1 Scenario Testing
323(7)
9.1.1 Deterministic Status Scenarios
324(1)
9.1.2 Stochastic Status Scenarios
325(3)
9.1.3 Stochastic Rate Scenarios
328(2)
9.2 Simulation Techniques
330(10)
9.2.1 Bootstrap Sampling
331(1)
9.2.2 Simulation Sampling
332(3)
9.2.3 Simulation Probabilities
335(2)
9.2.4 Simulation Prediction Intervals
337(3)
9.3 Investment Pricing Applications
340(3)
9.4 Stochastic Surplus Application
343(1)
9.5 Future Directions in Simulation Analysis
344(2)
Problems
346(2)
Excel Problems
348(2)
Solutions
350(3)
10 Further Statistical Considerations 353(22)
10.1 Mortality Adjustment Models
354(7)
10.1.1 Linear Mortality Acceleration Models
355(2)
10.1.2 Mean Mortality Acceleration Models
357(3)
10.1.3 Survival-Based Mortality Acceleration Models
360(1)
10.2 Mortality Trend Modeling
361(3)
10.3 Actuarial Statistics
364(6)
10.3.1 Normality-Based Prediction Intervals
365(1)
10.3.2 Prediction Set-Based Prediction Intervals
366(2)
10.3.3 Simulation-Based Prediction Intervals
368(2)
10.4 Data Set Simplifications
370(1)
Problems
371(1)
Excel Problems
371(2)
Solutions
373(2)
Appendix A: Excel Statistical Functions, Basic Mathematical Functions, and Add-Ins 375(2)
Appendix B: Acronyms and Principal Sections 377(2)
References 379(6)
Symbol Index 385(4)
Index 389
Dale S. Borowiak is a Professor Emeritus at the University of Akron, where he served for 35 years teaching statistics and initiating the actuarial science program. He received a Ph.D. from Bowling Green State University. His research has been published in professional journals in the fields of statistics, actuarial science, and engineering. He also published Model Discrimination for Nonlinear Regression Models, along with the first edition of the current text.

Arnold F. Shapiro is a Professor Emeritus at the Pennsylvania State University, where he was director of the actuarial program. He received a Ph. D. from the University of Pennsylvania (Wharton). He has published more than 100 articles in professional journals and two books. A Fellow of the Society of Actuaries and an Enrolled Actuary, he been a recipient of the Innovation in Teaching Award from the American Risk and Insurance Association and the Best Research Paper Award from the Health Section of the Society of Actuaries.