| ISBN |
9789400957817 |
| 기타 표준번호 |
10.1007/978-94-009-5781-7 |
| 청구기호 |
Q1-390 |
| 형태사항 |
XVI, 195 p. 19 illus. online resource.
|
| 언어 |
English |
| 내용 |
1. Definitions and Notations -- 1.1 The Purpose of the Theory of Risk -- 1.2 Random Processes in General -- 1.3. Positive and Negative Risk Sums -- 1.4. Main Problems -- 2. Process with Constant Size of One Claim -- 2.1. Introduction -- 2.2. The Poisson Process -- 2.3. Discussion of Assumptions -- 2.4. Numerical Calculations -- 2.5. Application 1 -- 2.6. Application 2 -- 3. Generalized Poisson Distribution -- 3.1. The Distribution Function of the Size of a Claim -- 3.2. Generalized Poisson Function -- 3.3. The Mean and Standard Deviation of F(x) -- 3.4. Characteristic Function -- 3.5. Estimation of S(z) -- 3.6. Decomposition of S(z) -- 4. Normal Approximation and Edgeworth Series for F(x) -- 4.1. The Normal Approximation -- 4.2. Edgeworth Series -- 4.3. Normal Power Expansion -- 4.4. The Accuracy of the Normal Approximation -- 5. Applications of the Normal Approximation -- 5.1. The Basic Equation -- 5.2. Net Retention -- 5.3. Reserve Funds -- 5.4. Statutory Basis of Reserve Funds -- 5.5. The Rule of Greatest Retention -- 5.6. The Case of Several M?�s -- 5.7. An Application to Insurance Statistics -- 5.8. Experience Rating, Credibility Theory -- 6. The Esscher Approximation -- 6.1. Introduction -- 6.2. The Accuracy of the Esscher Formula -- 6.3. Some Hints for Numerical Computations -- 6.4. Examples of Numerical Applications -- 7. Monte Carlo Method -- 7.1. Random Numbers -- 7.2. Simulation of Generalized Poisson Function -- 7.3. Discussion on the Accuracy and a Modification -- 8. Other Methods of Calculating the Generalized Poisson Function -- 8.1. Inversion of the Characteristic Function -- 8.2. A Modification of the Esscher Method -- 8.3. Step Function Approximation of S(z) -- 8.4. Exponent Polynomials -- 8.5. Mixed Methods -- 8.6. Statistical Method -- 9. Variance as a Measure of Stability -- 9.1. Optimum Form of Reinsurance -- 9.2. Reciprocity of Two Companies -- 10. Varying Basic Probabilities -- 10.1. Introduction -- 10.2. Compound Poisson Process -- 10.3. Direct Numerical Computation of the Compound Poisson Function -- 10.4. The Polya Process -- 10.5. Application to Stop Loss Reinsurance -- 11. The Ruin Probability During a Finite Time Period -- 11.1. The Ruin Function in Finite Time Periods -- 11.2. Calculation of ?N(U) by a Monte Carlo Method -- 12. The Ruin Probability During an Infinite Time Period -- 12.1. Introduction -- 12.2. Ruin Probability -- 12.3. Applications -- 12.4. Some Approximation Formulae -- 12.5. Discussion on the Different Methods -- 13. Application of Risk Theory to Business Planning -- Appendix A. Derivation of the Poisson Process and Compound Poisson Processes -- Appendix B. The Edgeworth Expansion -- Solutions to the Exercises -- Author Index.
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| 주제 |
Science.
Science, general.
Science, general.
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| 보유판 및 특별호 저록 |
Springer eBooks
Printed edition: 9789400957831
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| QR CODE |
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