Ruin probabilities /:
The book is a comprehensive treatment of classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (eg. for heavy-tailed claim size distributions), finite horizon ruin probabilities, exte...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
River Edge, NJ :
World Scientific,
2000
|
| Schriftenreihe: | Advanced series on statistical science & applied probability ;
v. 2. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The book is a comprehensive treatment of classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (eg. 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 or periodicity. Special features of the book are the emphasis on change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas like queueing theory. |
| Beschreibung: | 1 online resource (xi, 385 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9789812779311 9812779310 |
Internformat
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| 490 | 1 | |a Advanced series on statistical science & applied probability ; |v vol. 2 | |
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| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a I. Introduction. 1. The risk process -- 2. Claim size distributions -- 3. The arrival process -- 4. A summary of main results and methods -- 5. Conventions -- II. Some general tools and results. 1. Martingales -- 2. Likelihood ratios and change of measure -- 3. Duality with other applied probability models -- 4. Random walks in discrete or continuous time -- 5. Markov additive processes -- 6. The ladder height distribution -- III. 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 -- IV. 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? -- V. 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 queuing theory -- VI. 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 queuing models -- VII. Premiums depending on the current reserve. 1. Introduction -- 2. The model with interest -- 3. The local adjustment coefficient. Logarithmic asymptotics -- VIII. 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 -- IX. Ruin probabilities in the presence of heavy tails. 1. Subexponential distributions -- 2. The compound Poisson model -- 3. The renewal model -- 4. Models with dependent input -- 5. Finite horizon ruin probabilities -- 6. Reserve-dependent premiums -- X. Simulation methodology. 1. Generalities -- 2. Simulation via the Pollaczeck-Khinchine formula -- Importance sampling via Lundberg conjugation -- 4. Importance sampling for the finite horizon case -- 5. Regenerative simulation -- 6. Sensitivity analysis -- XI. Miscellaneous topics. 1. The ruin problem for Bernoulli random walk and Brownian motion. The two-barrier ruin problem -- 2. Further applications of martingales -- 3. Large deviations -- 4. The distribution of the aggregate claims -- 5. Principles for premium calculation -- 6. Reinsurance. | |
| 520 | |a The book is a comprehensive treatment of classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (eg. 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 or periodicity. Special features of the book are the emphasis on change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas like queueing theory. | ||
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| 650 | 2 | |a Risk |0 https://id.nlm.nih.gov/mesh/D012306 | |
| 650 | 6 | |a Assurance |x Mathématiques. | |
| 650 | 6 | |a Risque. | |
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| adam_text | |
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| contents | I. Introduction. 1. The risk process -- 2. Claim size distributions -- 3. The arrival process -- 4. A summary of main results and methods -- 5. Conventions -- II. Some general tools and results. 1. Martingales -- 2. Likelihood ratios and change of measure -- 3. Duality with other applied probability models -- 4. Random walks in discrete or continuous time -- 5. Markov additive processes -- 6. The ladder height distribution -- III. 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 -- IV. 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? -- V. 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 queuing theory -- VI. 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 queuing models -- VII. Premiums depending on the current reserve. 1. Introduction -- 2. The model with interest -- 3. The local adjustment coefficient. Logarithmic asymptotics -- VIII. 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 -- IX. Ruin probabilities in the presence of heavy tails. 1. Subexponential distributions -- 2. The compound Poisson model -- 3. The renewal model -- 4. Models with dependent input -- 5. Finite horizon ruin probabilities -- 6. Reserve-dependent premiums -- X. Simulation methodology. 1. Generalities -- 2. Simulation via the Pollaczeck-Khinchine formula -- Importance sampling via Lundberg conjugation -- 4. Importance sampling for the finite horizon case -- 5. Regenerative simulation -- 6. Sensitivity analysis -- XI. Miscellaneous topics. 1. The ruin problem for Bernoulli random walk and Brownian motion. The two-barrier ruin problem -- 2. Further applications of martingales -- 3. Large deviations -- 4. The distribution of the aggregate claims -- 5. Principles for premium calculation -- 6. Reinsurance. |
| ctrlnum | (OCoLC)827947385 |
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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? -- V. 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 queuing theory -- VI. 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 queuing models -- VII. Premiums depending on the current reserve. 1. Introduction -- 2. The model with interest -- 3. The local adjustment coefficient. Logarithmic asymptotics -- VIII. 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 -- IX. Ruin probabilities in the presence of heavy tails. 1. Subexponential distributions -- 2. The compound Poisson model -- 3. The renewal model -- 4. Models with dependent input -- 5. Finite horizon ruin probabilities -- 6. Reserve-dependent premiums -- X. Simulation methodology. 1. Generalities -- 2. Simulation via the Pollaczeck-Khinchine formula -- Importance sampling via Lundberg conjugation -- 4. Importance sampling for the finite horizon case -- 5. Regenerative simulation -- 6. Sensitivity analysis -- XI. Miscellaneous topics. 1. The ruin problem for Bernoulli random walk and Brownian motion. The two-barrier ruin problem -- 2. Further applications of martingales -- 3. Large deviations -- 4. The distribution of the aggregate claims -- 5. Principles for premium calculation -- 6. 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| id | ZDB-4-EBU-ocn827947385 |
| illustrated | Illustrated |
| indexdate | 2024-11-26T14:49:08Z |
| institution | BVB |
| isbn | 9789812779311 9812779310 |
| language | English |
| oclc_num | 827947385 |
| open_access_boolean | |
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| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xi, 385 pages) : illustrations |
| psigel | ZDB-4-EBU |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | World Scientific, |
| record_format | marc |
| series | Advanced series on statistical science & applied probability ; |
| series2 | Advanced series on statistical science & applied probability ; |
| spelling | Asmussen, Søren. Ruin probabilities / Søren Asmussen. River Edge, NJ : World Scientific, 2000 (2001 printing) 1 online resource (xi, 385 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Advanced series on statistical science & applied probability ; vol. 2 Includes bibliographical references and index. Print version record. I. Introduction. 1. The risk process -- 2. Claim size distributions -- 3. The arrival process -- 4. A summary of main results and methods -- 5. Conventions -- II. Some general tools and results. 1. Martingales -- 2. Likelihood ratios and change of measure -- 3. Duality with other applied probability models -- 4. Random walks in discrete or continuous time -- 5. Markov additive processes -- 6. The ladder height distribution -- III. 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 -- IV. 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? -- V. 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 queuing theory -- VI. 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 queuing models -- VII. Premiums depending on the current reserve. 1. Introduction -- 2. The model with interest -- 3. The local adjustment coefficient. Logarithmic asymptotics -- VIII. 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 -- IX. Ruin probabilities in the presence of heavy tails. 1. Subexponential distributions -- 2. The compound Poisson model -- 3. The renewal model -- 4. Models with dependent input -- 5. Finite horizon ruin probabilities -- 6. Reserve-dependent premiums -- X. Simulation methodology. 1. Generalities -- 2. Simulation via the Pollaczeck-Khinchine formula -- Importance sampling via Lundberg conjugation -- 4. Importance sampling for the finite horizon case -- 5. Regenerative simulation -- 6. Sensitivity analysis -- XI. Miscellaneous topics. 1. The ruin problem for Bernoulli random walk and Brownian motion. The two-barrier ruin problem -- 2. Further applications of martingales -- 3. Large deviations -- 4. The distribution of the aggregate claims -- 5. Principles for premium calculation -- 6. Reinsurance. The book is a comprehensive treatment of classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (eg. 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 or periodicity. Special features of the book are the emphasis on change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas like queueing theory. Insurance Mathematics. http://id.loc.gov/authorities/subjects/sh85066815 Risk. http://id.loc.gov/authorities/subjects/sh85114195 Risk https://id.nlm.nih.gov/mesh/D012306 Assurance Mathématiques. Risque. BUSINESS & ECONOMICS Insurance Risk Assessment & Management. bisacsh Insurance Mathematics fast Risk fast Waarschijnlijkheidstheorie. gtt Risicoanalyse. gtt Print version: Asmussen, Søren. Ruin probabilities. River Edge, NJ : World Scientific, 2000 (2001 printing) 9810222939 (DLC) 00038176 (OCoLC)43836603 Advanced series on statistical science & applied probability ; v. 2. http://id.loc.gov/authorities/names/n97121977 FWS01 ZDB-4-EBU FWS_PDA_EBU https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=512616 Volltext |
| spellingShingle | Asmussen, Søren Ruin probabilities / Advanced series on statistical science & applied probability ; I. Introduction. 1. The risk process -- 2. Claim size distributions -- 3. The arrival process -- 4. A summary of main results and methods -- 5. Conventions -- II. Some general tools and results. 1. Martingales -- 2. Likelihood ratios and change of measure -- 3. Duality with other applied probability models -- 4. Random walks in discrete or continuous time -- 5. Markov additive processes -- 6. The ladder height distribution -- III. 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 -- IV. 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? -- V. 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 queuing theory -- VI. 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 queuing models -- VII. Premiums depending on the current reserve. 1. Introduction -- 2. The model with interest -- 3. The local adjustment coefficient. Logarithmic asymptotics -- VIII. 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 -- IX. Ruin probabilities in the presence of heavy tails. 1. Subexponential distributions -- 2. The compound Poisson model -- 3. The renewal model -- 4. Models with dependent input -- 5. Finite horizon ruin probabilities -- 6. Reserve-dependent premiums -- X. Simulation methodology. 1. Generalities -- 2. Simulation via the Pollaczeck-Khinchine formula -- Importance sampling via Lundberg conjugation -- 4. Importance sampling for the finite horizon case -- 5. Regenerative simulation -- 6. Sensitivity analysis -- XI. Miscellaneous topics. 1. The ruin problem for Bernoulli random walk and Brownian motion. The two-barrier ruin problem -- 2. Further applications of martingales -- 3. Large deviations -- 4. The distribution of the aggregate claims -- 5. Principles for premium calculation -- 6. Reinsurance. Insurance Mathematics. http://id.loc.gov/authorities/subjects/sh85066815 Risk. http://id.loc.gov/authorities/subjects/sh85114195 Risk https://id.nlm.nih.gov/mesh/D012306 Assurance Mathématiques. Risque. BUSINESS & ECONOMICS Insurance Risk Assessment & Management. bisacsh Insurance Mathematics fast Risk fast Waarschijnlijkheidstheorie. gtt Risicoanalyse. gtt |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85066815 http://id.loc.gov/authorities/subjects/sh85114195 https://id.nlm.nih.gov/mesh/D012306 |
| title | Ruin probabilities / |
| title_auth | Ruin probabilities / |
| title_exact_search | Ruin probabilities / |
| title_full | Ruin probabilities / Søren Asmussen. |
| title_fullStr | Ruin probabilities / Søren Asmussen. |
| title_full_unstemmed | Ruin probabilities / Søren Asmussen. |
| title_short | Ruin probabilities / |
| title_sort | ruin probabilities |
| topic | Insurance Mathematics. http://id.loc.gov/authorities/subjects/sh85066815 Risk. http://id.loc.gov/authorities/subjects/sh85114195 Risk https://id.nlm.nih.gov/mesh/D012306 Assurance Mathématiques. Risque. BUSINESS & ECONOMICS Insurance Risk Assessment & Management. bisacsh Insurance Mathematics fast Risk fast Waarschijnlijkheidstheorie. gtt Risicoanalyse. gtt |
| topic_facet | Insurance Mathematics. Risk. Risk Assurance Mathématiques. Risque. BUSINESS & ECONOMICS Insurance Risk Assessment & Management. Insurance Mathematics Waarschijnlijkheidstheorie. Risicoanalyse. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=512616 |
| work_keys_str_mv | AT asmussensøren ruinprobabilities |