The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber-Shiu functions and dependence.

lgrsnf/M_Mathematics/MV_Probability/Asmussen S., Albrecher H. Ruin probabilities (2ed., WS, 2010)(ISBN 9814282529)(O)(621s)_MV_.pdf

nexusstc/Ruin Probabilities/a4c0d477060933ca4f35e46f321391f4.pdf

zlib/Mathematics/Søren Asmussen/Ruin Probabilities_1300926.pdf

Matrix-analytic Methods: Theory And Applications - Proceedings Of The Fourth International Conference Theory and Applications

Søren Asmussen; Hansjörg Albrecher; ProQuest (Firm)

Asmussen, Soren; Albrecher, Hansjorg

Hansjörg Albrecher; Søren Asmussen

Soren Asmussen; Hansjorg Albrecher

Søren Asmussen, Hansjorg Albrecher

Asmussen, Søren

World Scientific Publishing Company

Advanced series on statistical science and applied probability -- v. 14, 2nd ed., New Jersey, New Jersey, 2010

Advanced series on statistical science & applied probability, v. 14, 2nd ed, Singapore ; Hackensack, NJ, ©2010

Advanced series on statistical science & applied probability, 2nd ed, Singapore ; Hackensack, N.J, c2010

World Scientific Publishing Company, Singapore, 2010

Singapore, Singapore

2, 20100909

Kolxo3 -- 41-56

lg858790

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Includes bibliographical references and index.

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

<p>The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially updated and extended second version, new topics include stochastic control, fluctuation theory for Levy Processes, Gerber-Shiu functions and dependence.</p>

The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramer-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber-Shiu functions and dependence

The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality the Cram r-Lundberg approximation exact solutions other approximations (e.g. for heavy-tailed claim size distributions) finite horizon ruin probabilities extensions of the classical compound Poisson model to allow for reserve-dependent premiums Markov-modulation periodicity change of measure techniques phase-type distributions as a computational vehicle and the connection to other applied probability areas like queueing theory. In this substantially updated and extended second version new topics include stochastic control fluctuation theory for Levy processes Gerber-Shiu functions and dependence.

Introduction
Martingales and simple ruin calculations
Further general tools and results
The compound Poisson model
The probability of ruin within finite time
Renewal arrivals
Risk theory in a Markovian environment
Level-dependent risk processes
Matrix-analytic methods
Ruin probabilities in the presence of heavy tails
Ruin probabilities for Lévy processes
Gerber-Shiu functions
Further models with dependency
Stochastic control
Simulation methodology
Miscellaneous topics.

Offers a comprehensive treatment of the classical and modern ruin probability theory. This title includes topics such as: Lundberg's inequality, the Cramer-Lundberg approximation, exact solutions, other approximations, finite horizon ruin probabilities, and extensions of the classical compound Poisson model to allow for reserve-dependent premiums.

2012-08-21