Author | Willmot, Gordon E. author |
---|---|
Title | Lundberg Approximations for Compound Distributions with Insurance Applications [electronic resource] / by Gordon E. Willmot, X. Sheldon Lin |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2001 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-0111-0 |
Descript | X, 250 p. online resource |
1 Introduction -- 2 Reliability background -- 2.1 The failure rate -- 2.2 Equilibrium distributions -- 2.3 The residual lifetime distribution and its mean -- 2.4 Other classes of distributions -- 2.5 Discrete reliability classes -- 2.6 Bounds on ratios of discrete tail probabilities -- 3 Mixed Poisson distributions -- 3.1 Tails of mixed Poisson distributions -- 3.2 The radius of convergence -- 3.3 Bounds on ratios of tail probabilities -- 3.4 Asymptotic tail behaviour of mixed Poisson distributions -- 4 Compound distributions -- 4.1 Introduction and examples -- 4.2 The general upper bound -- 4.3 The general lower bound -- 4.4 A Wald-type martingale approach -- 5 Bounds based on reliability classifications -- 5.1 First order properties -- 5.2 Bounds based on equilibrium properties -- 6 Parametric Bounds -- 6.1 Exponential bounds -- 6.2 Pareto bounds -- 6.3 Product based bounds -- 7 Compound geometric and related distributions -- 7.1 Compound modified geometric distributions -- 7.2 Discrete compound geometric distributions -- 7.3 Application to ruin probabilities -- 7.4 Compound negative binomial distributions -- 8 Tijms approximations -- 8.1 The asymptotic geometric case -- 8.2 The modified geometric distribution -- 8.3 Transform derivation of the approximation -- 9 Defective renewal equations -- 9.1 Some properties of defective renewal equations -- 9.2 The time of ruin and related quantities -- 9.3 Convolutions involving compound geometric distributions -- 10 The severity of ruin -- 10.1 The associated defective renewal equation -- 10.2 A mixture representation for the conditional distribution -- 10.3 Erlang mixtures with the same scale parameter -- 10.4 General Erlang mixtures -- 10.5 Further results -- 11 Renewal risk processes -- 11.1 General properties of the model -- 11.2 The Coxian-2 case -- 11.3 The sum of two exponentials -- 11.4 Delayed and equilibrium renewal risk processes -- Symbol Index -- Author Index