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E-grāmata: Gerber-Shiu Risk Theory

  • Formāts: PDF+DRM
  • Sērija : EAA Series
  • Izdošanas datums: 02-Oct-2013
  • Izdevniecība: Springer International Publishing AG
  • Valoda: eng
  • ISBN-13: 9783319023038
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Gerber-Shiu Risk TheoryPalielināt
  • Formāts: PDF+DRM
  • Sērija : EAA Series
  • Izdošanas datums: 02-Oct-2013
  • Izdevniecība: Springer International Publishing AG
  • Valoda: eng
  • ISBN-13: 9783319023038
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Motivated by the many and long-standing contributions of H. Gerber and E. Shiu, this book gives a modern perspective on the problem of ruin for the classical CramérLundberg model and the surplus of an insurance company. The book studies martingales and path decompositions, which are the main tools used in analysing the distribution of the time of ruin, the wealth prior to ruin and the deficit at ruin. Recent developments in exotic ruin theory are also considered. In particular, by making dividend or tax payments out of the surplus process, the effect on ruin is explored.

Gerber-Shiu Risk Theory can be used as lecture notes and is suitable for a graduate course. Each chapter corresponds to approximately two hours of lectures.

Recenzijas

From the book reviews:

The book under review gives a modern perspective on the problems in ruin theory in the framework of the classical Cramér-Lundberg risk model. This compact book combines rigorous mathematical treatments with discussions and contains a comprehensive bibliography on the related topics at the end of each chapter. this book is well written and can serve as a major reference book for researchers and graduate students in ruin  theory and related areas. (Shuanming Li, Mathematical Reviews, January, 2015)

1 Introduction
1(8)
1.1 The Cramer-Lundberg Process
1(2)
1.2 The Classical Problem of Ruin
3(1)
1.3 Gerber-Shiu Expected Discounted Penalty Functions
4(1)
1.4 Exotic Gerber-Shiu Theory
5(2)
1.5 Comments
7(2)
2 The Wald Martingale and the Maximum
9(8)
2.1 Laplace Exponent
9(2)
2.2 First Exponential Martingale
11(1)
2.3 Esscher Transform
12(2)
2.4 Distribution of the Maximum
14(1)
2.5 Comments
15(2)
3 The Kella-Whitt Martingale and the Minimum
17(10)
3.1 The Cramer--Lundberg Process Reflected in Its Supremum
17(1)
3.2 A Useful Poisson Integral
18(3)
3.3 Second Exponential Martingale
21(1)
3.4 Duality
22(2)
3.5 Distribution of the Minimum
24(1)
3.6 The Long-Term Behaviour
25(1)
3.7 Comments
25(2)
4 Scale Functions and Ruin Probabilities
27(10)
4.1 Scale Functions and the Probability of Ruin
27(3)
4.2 Connection with the Pollaczek--Khintchine Formula
30(3)
4.3 Gambler's Ruin
33(2)
4.4 Comments
35(2)
5 The Gerber-Shiu Measure
37(8)
5.1 Decomposing Paths at the Minimum
37(1)
5.2 Resolvent Densities
38(2)
5.3 More on Poisson Integrals
40(1)
5.4 Gerber-Shiu Measure and Gambler's Ruin
41(2)
5.5 Comments
43(2)
6 Reflection Strategies
45(12)
6.1 Perpetuities
46(1)
6.2 Decomposing Paths at the Maximum
47(4)
6.3 Derivative of the Scale Function
51(2)
6.4 Present Value of Dividends Paid Until Ruin
53(1)
6.5 Comments
54(3)
7 Perturbation-at-Maximum Strategies
57(10)
7.1 Rehung Excursions
57(2)
7.2 Marked Poisson Process Revisited
59(2)
7.3 Gambler's Ruin for the Perturbed Process
61(2)
7.4 Continuous Ruin with Heavy Perturbation
63(1)
7.5 Expected Present Value of Tax at Ruin
64(1)
7.6 Comments
65(2)
8 Refraction Strategies
67(12)
8.1 Pathwise Existence and Uniqueness
67(3)
8.2 Gambler's Ruin and Resolvent Density
70(5)
8.3 Resolvent Density with Ruin
75(2)
8.4 Comments
77(2)
9 Concluding Discussion
79(12)
9.1 Mixed-Exponential Claims
79(2)
9.2 Spectrally Negative Levy Processes
81(3)
9.3 Analytic Properties of Scale Functions
84(1)
9.4 Engineered Scale Functions
85(4)
9.5 Comments
89(2)
References 91
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