Preface
Notation and conventions
I　Introduction
　1　The risk process
　2　Claim size distributions
　3　The arrival process
　4　A summary of main results and methods
II　Martingales and simple ruin calculations
　1　Wald martingales
　2　Gambler's ruin. Two-sided ruin. Brownian motion
　3　Further simple martingale calculations
　4　More advanced martingales
III　Further general tools and results
　1　Likelihood ratios and change of measure
　2　Duality with other applied probability models
　3　Random walks in discrete or continuous time
　4　Markov additive processes
　5　The ladder height distribution
IV　The compound Poisson model
　1　Introduction
　2　The Pollaczeck-Khinchine formula
　3　Special cases of the Pollaczeck-Khinchine formula
　4　Change of measure via exponential families
　5　Lundberg conjugation
　6　Further topics related to the adjustment coefficient
　7　Various approximations for the ruin probability
　8　Comparing the risks of different claim size distributions
　9　Sensitivity estimates
　10　Estimation of the adjustment coefficient
V　The probability of ruin within finite time
　1　Exponential claims
　2　The ruin probability with no initial reserve
　3　Laplace transforms
　4　When does ruin occur?
　5　Diffusion approximations
　6　Corrected diffusion approximations
　7　How does ruin occur?
VI　Renewal arrivals
　1　Introduction
　2　Exponential claims. The compound Poisson model with negative claims
　3　Change of measure via exponential families
　4　The duality with queueing theory
VII　Risk theory in a Markovian environment
　1　Model and examples
　2　The ladder height distribution
　3　Change of measure via exponential families
　4　Comparisons with the compound Poisson model
　5　The Markovian arrival process
　6　Risk theory in a periodic environment
　7　Dual queueing models
VIII Level-dependent risk processes
　1　Introduction
　2　The model with constant interest
　3　The local adjustment coefficient. Logarithmic asymptotics
　4　The model with tax
　5　Discrete-time ruin problems with stochastic investment
　6　Continuous-time ruin problems with stochastic investment
IX　Matrix-analytic methods
　1　Definition and basic properties of phase-type distributions
　2　Renewal theory
　3　The compound Poisson model
　4　The renewal model
　5　Markov-modulated input
　6　Matrix-exponential distributions
　7　Reserve-dependent premiums
　8　Erlangization for the finite horizon case
X　Ruin probabilities in the presence of heavy tails
　1　Subexponential distributions
　2　The compound Poisson model
　3　The renewal model
　4　Finite-horizon ruin probabilities
　5　Reserve-dependent premiums
　6　Tail estimation
XI　Ruin probabilities for Levy processes
　1　Preliminaries
　2　One-sided ruin theory
　3　The scale function and two-sided ruin problems
　4　Further topics
　5　The scale function for two-sided phase-type jumps
XII　Gerber-Shiu functions
　1　Introduction
　2　The compound Poisson model
　3　The renewal model
　4　Levy risk models
XIII Further models with dependence
　1　Large deviations
　2　Heavy-tailed risk models with dependent input
　3　Linear models
　4　Risk processes with shot-noise Cox intensities
　5　Causal dependency models
　6　Dependent Sparre Andersen models
　7　Gaussian models. Fractional Brownian motion
　8　Ordering of ruin probabilities
　9　Multi-dimensional risk processes
XIV Stochastic control
　1　Introduction
　2　Stochastic dynamic programming
　3　The Hamilton-Jacobi-Bellman equation
XV　Simulation methodology
　1　Generalities
　2　Simulation via the Pollaczeck-Khinchine formula...
　3　Static importance sampling via Lundberg conjugation
　4　Static importance sampling for the finite horizon case
　5　Dynamic importance sampling
　6　Regenerative simulation
　7　Sensitivity analysis
XVI Miscellaneous topics
　1　More on discrete-time risk models
　2　The distribution of the aggregate claims
　3　Principles for premium calculation
　4　Reinsurance
Appendix
　A1　Renewal theory
　A2　Wiener-Hopf factorization
　A3　Matrix-exponentials
　A4　Some linear algebra
　A5　Complements on phase-type distributions
　A6　Tauberian theorems
Bibliography
Index