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Risk and Insurance: A Graduate Text 2020 ed. [Kõva köide]

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  • Formaat: Hardback, 505 pages, kõrgus x laius: 235x155 mm, kaal: 945 g, 32 Illustrations, color; 10 Illustrations, black and white; XV, 505 p. 42 illus., 32 illus. in color., 1 Hardback
  • Sari: Probability Theory and Stochastic Modelling 96
  • Ilmumisaeg: 18-Apr-2020
  • Kirjastus: Springer Nature Switzerland AG
  • ISBN-10: 3030351750
  • ISBN-13: 9783030351755
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Risk and Insurance: A Graduate Text 2020 ed.Suurem pilt
  • Formaat: Hardback, 505 pages, kõrgus x laius: 235x155 mm, kaal: 945 g, 32 Illustrations, color; 10 Illustrations, black and white; XV, 505 p. 42 illus., 32 illus. in color., 1 Hardback
  • Sari: Probability Theory and Stochastic Modelling 96
  • Ilmumisaeg: 18-Apr-2020
  • Kirjastus: Springer Nature Switzerland AG
  • ISBN-10: 3030351750
  • ISBN-13: 9783030351755
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783030351755.html
Märksõnad:

This textbook provides a broad overview of the present state of insurance mathematics and some related topics in risk management, financial mathematics and probability. Both non-life and life aspects are covered. The emphasis is on probability and modeling rather than statistics and practical implementation. Aimed at the graduate level, pointing in part to current research topics, it can potentially replace other textbooks on basic non-life insurance mathematics and advanced risk management methods in non-life insurance. Based on chapters selected according to the particular topics in mind, the book may serve as a source for introductory courses to insurance mathematics for non-specialists, advanced courses for actuarial students, or courses on probabilistic aspects of risk.  It will also be useful for practitioners and students/researchers in related areas such as finance and statistics who wish to get an overview of the general area of mathematical modeling and analysis in insurance.



Chapter I Basics
1(24)
1 Actuarial Versus Financial Pricing
1(4)
2 Utility
5(7)
3 Premium Rules
12(2)
4 Reinsurance
14(2)
5 Poisson Modelling
16(9)
Chapter II Experience Rating
25(26)
1 Bayes and Empirical Bayes
25(5)
2 Exponential Families and Conjugate Priors
30(3)
3 Credibility Premiums
33(10)
4 Bonus-Malus Systems
43(8)
Chapter III Sums and Aggregate Claims
51(34)
1 Introduction
51(5)
2 Heavy Tails. Subexponential Distributions
56(8)
3 Large Deviations of Sums of Light-Tailed Random Variables
64(5)
4 Tails of Sums of Light-Tailed Random Variables
69(4)
5 Aggregate Claims and Compound Sums: Generalities
73(3)
6 Panjer's Recursion
76(3)
7 Tails of Compound Sums
79(6)
Chapter IV Ruin Theory
85(28)
1 The Cramer-Lundberg Model
85(3)
2 First Results: Martingale Techniques
88(2)
3 Ladder Heights. Heavy Tails
90(3)
4 Proof of the Cramer-Lundberg Approximation
93(3)
5 Finite Time Ruin Probabilities
96(5)
6 Markov Regime Switching
101(5)
7 Level-Dependent Premiums
106(3)
8 The Diffusion Approximation
109(4)
Chapter V Markov Models in Life Insurance
113(28)
1 The Contract Payments and the Probability Model
113(1)
2 Canonical Models
114(11)
3 Valuation of the Payments
125(9)
4 Valuation in Canonical Models
134(7)
Chapter VI Financial Mathematics in Life Insurance
141(48)
1 Background and Simple Claims
142(9)
2 Payment Streams
151(4)
3 Unit-Link Insurance
155(10)
4 With-Profit Insurance and the Dynamics of the Surplus
165(6)
5 Cash Dividends and Market Reserve
171(2)
6 The Pure Case of Cash Dividends
173(2)
7 Bonus Payments and Market Reserve
175(6)
8 The Pure Case of Bonus Payments
181(2)
9 Comparison of Products
183(6)
Chapter VII Special Studies in Life Insurance
189(58)
1 Duration-Dependent Intensities and Payments
189(4)
2 Reserve-Dependent Payments and Intensities
193(6)
3 Bonds and Forward Interest Rates
199(3)
4 Survival Probabilities and Forward Mortality Rates
202(6)
5 Dependent Interest and Mortality Rates
208(3)
6 Stochastic Interest and Mortality Rate Models
211(8)
7 Reserves Revisited
219(2)
8 Incidental Policy Holder Behavior
221(8)
9 Rational Policy Holder Behavior
229(10)
10 Higher Order Moments. Hattendorf's Theorem
239(8)
Chapter VIII Orderings and Comparisons
247(28)
1 Stochastic Ordering of Risks
247(2)
2 Convex and Increasing Convex Ordering
249(10)
3 Closure Properties of Orderings
259(2)
4 Utility, Deductibles and Reinsurance
261(7)
5 Applications to Ruin Theory
268(1)
6 Maximizing the Adjustment Coefficient
269(6)
Chapter IX Extreme Value Theory
275(24)
1 Introduction
275(1)
2 Elementary Examples and Considerations
276(4)
3 Convergence Results
280(10)
4 Proof of the Fisher-Tippett Theorem
290(2)
5 Records
292(7)
Chapter X Dependence and Further Topics in Risk Management
299(56)
1 Risk Measures
300(8)
2 The Frechet-Hoffding Bounds. Comonotonicity
308(5)
3 Special Dependence Structures
313(7)
4 Copulas
320(7)
5 Pearson, Kendall and Spearman
327(5)
6 Further Dependence Concepts
332(4)
7 Tails of Sums of Dependent Risks
336(6)
8 Dependence Orderings
342(13)
Chapter XI Stochastic Control in Non-Life Insurance
355(32)
1 Introduction
355(4)
2 Minimizing the Ruin Probability
359(7)
3 The Hamilton-Jacobi-Bellman Equation
366(4)
4 Optimal Dividends
370(3)
5 Control Problems for the Cramer-Lundberg Model
373(8)
6 Examples Involving Game Theory
381(6)
Chapter XII Stochastic Control in Life Insurance
387(46)
1 The Diffusion Approximation
388(6)
2 Finite-State Markov Process Linear Regulation
394(6)
3 The Consumption-Investment Problem
400(8)
4 Uncertain Lifetime
408(5)
5 The Consumption-Investment-Insurance Problem
413(4)
6 The Multi-State Problem
417(9)
7 The Pension Fund's Problem
426(7)
Chapter XIII Selected Further Topics
433(32)
1 Claims Reserving
433(6)
2 Multivariate Extreme Value Theory
439(3)
3 Statistical Methods for Tails and Extreme Values
442(4)
4 Large Deviations Theory in Function Spaces
446(11)
5 Gaussian Maxima
457(8)
Appendix
465(28)
A.1 Integral Formulas
465(2)
A.2 Differential Equations
467(4)
A.3 Inhomogeneous Markov Processes
471(4)
A.4 Ito's Formula
475(2)
A.5 Diffusion First Passage Probabilities
477(1)
A.6 Z-2 Projections. Least Squares. Conditional Expectations
478(3)
A.7 Supplements on the Normal Distribution
481(3)
A.8 Generalized Inverses
484(3)
A.9 The Distributional Transform
487(1)
A.10 Types of Distributions
488(2)
A.11 Transforms
490(3)
References 493(8)
Index 501
Søren Asmussen obtained his PhD at the University of Copenhagen in 1978, followed by the Danish degree of Dr. scient. in 1982. He held academic positions at the University of Copenhagen before moving to Aalborg University in 1987, where he received one of the prestigious Danish research professorships in 1990. In 1995, he became Professor of Mathematical Statistics at Lund University in Sweden, and then moved to his current position as Professor of Applied Probability at Aarhus University in Denmark in 2003. He received the Marcel F. Neuts Applied Probability Prize in 1999, the INFORMS Outstanding Publication Prizes in Simulation in 2002 and 2008, the John von Neumann Theory Prize in 2010, and the gold medal "For Great Contributions in Mathematics" from the Sobolev Institute of Mathematics, Russian Academy of Sciences in 2011.









Mogens Steffensen, University of Copenhagen