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AuthorSchmidt, Klaus D. author
TitleLectures on Risk Theory [electronic resource] / by Klaus D. Schmidt
ImprintWiesbaden : Vieweg+Teubner Verlag, 1996
Connect tohttp://dx.doi.org/10.1007/978-3-322-90570-3
Descript X, 200p. online resource

SUMMARY

"... Especially now, where from the side of mathematical finance interest is also shown for insurance-related products, a book like this one will definitely be instrumental in communicating the basic mathematical models to non-experts in insurance. I therefore welcome this book for its intended audience." P. Embrechts. Mathematical Reviews, Ann Arbor "... [The book] is useful as a detailed theoretical complement to one of the classical introductory texts on risk theory ...". M. Schweizer. Zentralblatt fรผr Mathematik, Berlin "... The author's goals are clearly proclaimed at the outset, and they are pursued with persistence and integrity. The result is a book which is an integral whole, original in some respects, with interesting contributions. And no errors - not even a single misprint. I recommend it to every tutor of risk theory as a source of mathematically solid proofs and complete explorations of certain aspects of the subject." R. Norberg. Metrika, Heidelberg


CONTENT

1 The Claim Arrival Process -- 1.1 The Model -- 1.2 The Erlang Case -- 1.3 A Characterization of the Exponential Distribution -- 1.4 Remarks -- 2 The Claim Number Process -- 2.1 The Model -- 2.2 The Erlang Case -- 2.3 A Characterization of the Poisson Process -- 2.4 Remarks -- 3 The Claim Number Process as a Markov Process -- 3.1 The Model -- 3.2 A Characterization of Regularity -- 3.3 A Characterization of the Inhomogeneous Poisson Process -- 3.4 A Characterization of Homogeneity -- 3.5 A Characterization of the Poisson Process -- 3.6 A Claim Number Process with Contagion -- 3.7 Remarks -- 4 The Mixed Claim Number Process -- 4.1 The Model -- 4.2 The Mixed Poisson Process -- 4.3 The Pรณlya-Lundberg Process -- 4.4 Remarks -- 5 The Aggregate Claims Process -- 5.1 The Model -- 5.2 Compound Distributions -- 5.3 A Characterization of the Binomial, Poisson, and Negativebinomial Distributions -- 5.4 The Recursions of Panjer and DePril -- 5.5 Remarks -- 6 The Risk Process in Reinsurance -- 6.1 The Model -- 6.2 Thinning a Risk Process -- 6.3 Decomposition of a Poisson Risk Process -- 6.4 Superposition of Poisson Risk Processes -- 6.5 Remarks -- 7 The Reserve Process and the Ruin Problem -- 7.1 The Model -- 7.2 Kolmogorovโ{128}{153}s Inequality for Positive Supermartingales -- 7.3 Lundbergโ{128}{153}s Inequality -- 7.4 On the Existence of a Superadjustment Coefficient -- 7.5 Remarks -- Appendix: Special Distributions -- Auxiliary Notions -- Measures -- Generalities on Distributions -- Discrete Distributions -- Continuous Distributions -- List of Symbols -- Author Index


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