Author | Schmidt, Klaus D. author |
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Title | Lectures on Risk Theory [electronic resource] / by Klaus D. Schmidt |
Imprint | Wiesbaden : Vieweg+Teubner Verlag, 1996 |
Connect to | http://dx.doi.org/10.1007/978-3-322-90570-3 |
Descript | X, 200p. online resource |
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 Kolmogorovโs Inequality for Positive Supermartingales -- 7.3 Lundbergโs 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