Aspects of Risk Theory

1 The classical risk model.- 1.1 Ruin probabilities for the classical risk process.- 1.2 “Practical” evaluation of ruin probabilities.- 1.3 Inference for the risk process.- 2 Generalizations of the classical risk model.- 2.1 Models allowing for size fluctuation.- 2.2 Models allowing for risk fluctuation.- 3 Renewal models.- 3.1 Ordinary renewal models.- 3.2 Stationary renewal models.- 3.3 Numerical illustrations.- 4 Cox models.- 4.1 Markovian intensity: Preliminaries.- 4.2 The martingale approach.- 4.3 Independent jump intensity.- 4.3.1 An inbedded random walk.- 4.3.2 Ordinary independent jump intensity.- 4.3.3 Stationary independent jump intensity.- 4.4 Markov renewal intensity.- 4.5 Markovian intensity.- 4.5.1 Application of the basic approach.- 4.5.2 An alternative approach.- 4.6 Numerical illustrations.- 5 Stationary models.- Appendix. Finite time ruin probabilities.- A.1 The classical model.- A.2 Renewal models.- A.3 Cox models.- A.4 Diffusion approximations.- References and author index.- Inserted surveys.- Basic martingale theory.- Basic facts about weak convergence.- Point processes and martingales.- Point processes and random measures.- Basic definitions.- Superposition of point processes.- Thinning of point processes.- Basic Markov process theory.- Stationary point processes.