| Preface | p. ix |
| Notation and conventions | p. xiii |
| Introduction | p. 1 |
| The risk process | p. 1 |
| Claim size distributions | p. 6 |
| The arrival process | p. 11 |
| A summary of main results and methods | p. 13 |
| Martingales and simple ruin calculations | p. 21 |
| Wald martingales | p. 21 |
| Gambler's ruin. Two-sided ruin. Brownian motion | p. 23 |
| Further simple martingale calculations | p. 29 |
| More advanced martingales | p. 30 |
| Further general tools and results | p. 39 |
| Likelihood ratios and change of measure | p. 39 |
| Duality with other applied probability models | p. 45 |
| Random walks in discrete or continuous time | p. 48 |
| Markov additive processes | p. 54 |
| The ladder height distribution | p. 62 |
| The compound Poisson model | p. 71 |
| Introduction | p. 72 |
| The Pollaczeck-Khinchine formula | p. 75 |
| Special cases of the Pollaczeck-Khinchine formula | p. 77 |
| Change of measure via exponential families | p. 82 |
| Lundberg conjugation | p. 84 |
| Further topics related to the adjustment coefficient | p. 91 |
| Various approximations for the ruin probability | p. 95 |
| Comparing the risks of different claim size distributions | p. 100 |
| Sensitivity estimates | p. 103 |
| Estimation of the adjustment coefficient | p. 100 |
| The probability of ruin within finite time | p. 115 |
| Exponential claims | p. 116 |
| The ruin probability with no initial reserve | p. 121 |
| Laplace transforms | p. 126 |
| When does ruin occur? | p. 128 |
| Diffusion approximations | p. 136 |
| Corrected diffusion approximations | p. 139 |
| How does ruin occur? | p. 146 |
| Renewal arrivals | p. 151 |
| Introduction | p. 151 |
| Exponential claims. The compound Poisson model with negative claims | p. 154 |
| Change of measure via exponential families | p. 157 |
| The duality with queueing theory | p. 161 |
| Risk theory in a Markovian Environment | p. 165 |
| Model and examples | p. 165 |
| The ladder height distribution | p. 172 |
| Change of measure via exponential families | p. 180 |
| Comparisons with the compound Poisson model | p. 188 |
| The Markovian arrival process | p. 194 |
| Risk theory in a periodic environment | p. 196 |
| Dual queueing models | p. 205 |
| Level-dependent risk processes | p. 209 |
| Introduction | p. 209 |
| The model with constant interest | p. 222 |
| The local adjustment coefficient. Logarithmic asymptotics | p. 227 |
| The model with tax | p. 239 |
| Discrete-time ruin problems with stochastic investment | p. 242 |
| Continuous-time ruin problems with stochastic investment | p. 248 |
| Matrix-analytic methods | p. 253 |
| Definition and basic properties of phase-type distributions | p. 253 |
| Renewal theory | p. 260 |
| The compound Poisson model | p. 264 |
| The renewal model | p. 266 |
| Markov-modulated input | p. 271 |
| Matrix-exponential distributions | p. 277 |
| Reserve-dependent premiums | p. 281 |
| Erlangization for the finite horizon case | p. 287 |
| Ruin probabilities in the presence of heavy tails | p. 293 |
| Subexponential distributions | p. 293 |
| The compound Poisson model | p. 302 |
| The renewal model | p. 305 |
| Finite-horizon ruin probabilities | p. 309 |
| Reserve-dependent premiums | p. 318 |
| Tail estimation | p. 320 |
| Ruin probabilities for Lévy processes | p. 329 |
| Preliminaries | p. 329 |
| One-sided ruin theory | p. 336 |
| The scale function and two-sided ruin problems | p. 340 |
| Further topics | p. 345 |
| The scale function for two-sided phase-type jumps | p. 353 |
| Gerber-Shiu functions | p. 357 |
| Introduction | p. 357 |
| The compound Poisson model | p. 360 |
| The renewal model | p. 374 |
| Lévy risk models | p. 384 |
| Further models with dependence | p. 397 |
| Large deviations | p. 398 |
| Heavy-tailed risk models with dependent input | p. 410 |
| Linear models | p. 417 |
| Risk processes with shot-noise Cox intensities | p. 419 |
| Causal dependency models | p. 424 |
| Dependent Sparre Andersen models | p. 427 |
| Gaussian models. Fractional Brownian motion | p. 428 |
| Ordering of ruin probabilities | p. 433 |
| Multi-dimensional risk processes | p. 435 |
| Stochastic control | p. 445 |
| Introduction | p. 445 |
| Stochastic dynamic programming | p. 447 |
| The Hamilton-Jacobi-Bellman equation | p. 448 |
| Simulation methodology | p. 461 |
| Generalities | p. 461 |
| Simulation via the Pollaczeck-Khinchine formula | p. 465 |
| Static importance sampling via Lundberg conjugation | p. 470 |
| Static importance sampling for the finite horizon case | p. 474 |
| Dynamic importance sampling | p. 475 |
| Regenerative simulation | p. 482 |
| Sensitivity analysis | p. 484 |
| Miscellaneous topics | p. 487 |
| More on discrete-time risk models | p. 487 |
| The distribution of the aggregate claims | p. 493 |
| Principles for premium calculation | p. 510 |
| Reinsurance | p. 513 |
| Appendix | p. 517 |
| Renewal theory | p. 517 |
| Wiener-Hopf factorization | p. 522 |
| Matrix-exponentials | p. 526 |
| Some linear algebra | p. 530 |
| Complements on phase-type distributions | p. 536 |
| Tauberian theorems | p. 548 |
| Bibliography | p. 549 |
| Index | p. 597 |
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