Ruin probabilities /
Guardat en:
| Autor principal: | |
|---|---|
| Format: | Llibre |
| Idioma: | English |
| Publicat: |
River Edge, NJ :
World Scientific,
c2000.
|
| Col·lecció: | Advanced series on statistical science & applied probability ;
vol. 2. |
| Matèries: |
Taula de continguts:
- I. Introduction
- II. Some general tools and results
- Martingales
- Likelihood ratios and change of measure
- Duality with other applied probability models
- Random walks in discrete or continuous time
- Markov additive processes
- The ladder height distribution
- III. The compound Poisson model
- The Pollaczeck-Khinchine formula
- Special cases of the Pollaczeck-Khinchine formula
- Change of measure via exponential families
- Lundberg conjugation
- Further topics related to the adjustment coefficient
- Various approximations for the ruin probability
- Comparing the risks of different claim size distributions
- Sensitivity estimates
- Estimation of the adjustment coefficient
- IV. The probability of ruin within finite time
- Exponential claims
- The ruin probability with no initial reserve
- Laplace transforms
- When does ruin occur?
- Diffusion approximations
- Corrected diffusion approximations
- How does ruin occur?
- V. Renewal arrivals
- Exponential claims. The compound Poisson model with negative claims
- Change of measure via exponential families
- The duality with queueing theory
- VI. Risk theory in a Markovian environment
- Model and examples
- The ladder height distribution
- Change of measure via exponential families
- Comparisons with the compound Poisson model
- The Markovian arrival process
- Risk theory in a periodic environment
- Dual queueing models
- VII. Premiums depending on the current reserve
- The model with interest
- The local adjustment coefficient. Logarithmic asymptotics
- VIII. Matrix-analytic methods
- Definition and basic properties of phase-type distributions
- Renewal theory
- The compound Poisson model
- The renewal model
- Markov-modulated input
- Matrix-exponential distributions
- Reserve-dependent premiums
- IX. Ruin probabilities in the presence of heavy tails
- Subexponential distributions
- The compound Poisson model
- The renewal model
- Models with dependent input
- Finite-horizon ruin probabilities
- Reserve-dependent premiums
- X. Simulation methodology
- Generalities
- Simulation via the Pollaczeck-Khinchine formula
- Importance sampling via Lundberg conjugation
- Importance sampling for the finite horizon case
- Regenerative simulation
- Sensitivity analysis
- XI. Miscellaneous topics
- The ruin problem for Bernoulli random walk and Brownian motion. The two-barrier ruin problem
- Further applications of martingales
- Large deviations
- The distribution of the aggregate claims
- Principles for premium calculation
- Reinsurance
- App. A1. Renewal theory
- App. A2. Wiener-Hopf factorization
- App. A3. Matrix-exponentials
- App. A4. Some linear algebra
- App. A5. Complements on phase-type distributions.