| Preface | |
| Introduction | p. 1 |
| Some general tools and results | p. 23 |
| Martingales | p. 24 |
| Likelihood ratios and change of measure | p. 26 |
| Duality with other applied probability models | p. 30 |
| Random walks in discrete or continuous time | p. 33 |
| Markov additive processes | p. 39 |
| The ladder height distribution | p. 47 |
| The compound Poisson model | p. 57 |
| The Pollaczeck-Khinchine formula | p. 61 |
| Special cases of the Pollaczeck-Khinchine formula | p. 62 |
| Change of measure via exponential families | p. 67 |
| Lundberg conjugation | p. 69 |
| Further topics related to the adjustment coefficient | p. 75 |
| Various approximations for the ruin probability | p. 79 |
| Comparing the risks of different claim size distributions | p. 83 |
| Sensitivity estimates | p. 86 |
| Estimation of the adjustment coefficient | p. 93 |
| The probability of ruin within finite time | p. 97 |
| Exponential claims | p. 98 |
| The ruin probability with no initial reserve | p. 103 |
| Laplace transforms | p. 108 |
| When does ruin occur? | p. 110 |
| Diffusion approximations | p. 117 |
| Corrected diffusion approximations | p. 121 |
| How does ruin occur? | p. 127 |
| Renewal arrivals | p. 131 |
| Exponential claims. The compound Poisson model with negative claims | p. 134 |
| Change of measure via exponential families | p. 137 |
| The duality with queueing theory | p. 141 |
| Risk theory in a Markovian environment | p. 145 |
| Model and examples | p. 145 |
| The ladder height distribution | p. 152 |
| Change of measure via exponential families | p. 160 |
| Comparisons with the compound Poisson model | p. 168 |
| The Markovian arrival process | p. 173 |
| Risk theory in a periodic environment | p. 176 |
| Dual queueing models | p. 185 |
| Premiums depending on the current reserve | p. 189 |
| The model with interest | p. 196 |
| The local adjustment coefficient. Logarithmic asymptotics | p. 201 |
| Matrix-analytic methods | p. 215 |
| Definition and basic properties of phase-type distributions | p. 215 |
| Renewal theory | p. 223 |
| The compound Poisson model | p. 227 |
| The renewal model | p. 229 |
| Markov-modulated input | p. 234 |
| Matrix-exponential distributions | p. 240 |
| Reserve-dependent premiums | p. 244 |
| Ruin probabilities in the presence of heavy tails | p. 251 |
| Subexponential distributions | p. 251 |
| The compound Poisson model | p. 259 |
| The renewal model | p. 261 |
| Models with dependent input | p. 264 |
| Finite-horizon ruin probabilities | p. 271 |
| Reserve-dependent premiums | p. 279 |
| Simulation methodology | p. 281 |
| Generalities | p. 281 |
| Simulation via the Pollaczeck-Khinchine formula | p. 285 |
| Importance sampling via Lundberg conjugation | p. 287 |
| Importance sampling for the finite horizon case | p. 290 |
| Regenerative simulation | p. 292 |
| Sensitivity analysis | p. 294 |
| Miscellaneous topics | p. 297 |
| The ruin problem for Bernoulli random walk and Brownian motion. The two-barrier ruin problem | p. 297 |
| Further applications of martingales | p. 304 |
| Large deviations | p. 306 |
| The distribution of the aggregate claims | p. 316 |
| Principles for premium calculation | p. 323 |
| Reinsurance | p. 326 |
| Renewal theory | p. 331 |
| Wiener-Hopf factorization | p. 336 |
| Matrix-exponentials | p. 340 |
| Some linear algebra | p. 344 |
| Complements on phase-type distributions | p. 350 |
| Bibliography | p. 363 |
| Index | p. 383 |
| Table of Contents provided by Blackwell. All Rights Reserved. |
