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Ruin probabilities : smoothness, bounds, supermartingale approach.
Ruin Probabilities: Smoothness, Bounds, Supermartingale Approach deals with continuous-time risk models and covers several aspects of risk theory. The first of them is the smoothness of the survival probabilities. In particular, the book provides a detailed investigation of the continuity and differ...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
[Place of publication not identified] :
Elsevier,
2016.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Mishura, Yuliya. | |
| 245 | 1 | 0 | |a Ruin probabilities : |b smoothness, bounds, supermartingale approach. |
| 260 | |a [Place of publication not identified] : |b Elsevier, |c 2016. | ||
| 300 | |a 1 online resource | ||
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| 505 | 0 | |a Front Cover ; Ruin Probabilities: Smoothness, Bounds, Supermartingale Approach ; Copyright; Contents; Preface; PART 1. SMOOTHNESS OF THE SURVIVAL PROBABILITIES WITH APPLICATIONS; Chapter 1. Classical Results on the Ruin Probabilities; 1.1. Classical risk model; 1.2. Risk model with stochastic premiums; Chapter 2. Classical Risk Model with Investments in a Risk-Free Asset; 2.1. Description of the model; 2.2. Continuity and differentiability of the infinite-horizon survival probability; 2.3. Continuity of the finite-horizon survival probability and existence of its partial derivatives. | |
| 505 | 8 | |a 2.4. Bibliographical notesChapter 3. Risk Model with Stochastic Premiums and Investments in a Risk-Free Asset; 3.1. Description of the model; 3.2. Continuity and differentiability of the infinite-horizon survival probability; 3.3. Continuity of the finite-horizon survival probability and existence of its partial derivatives; Chapter 4. Classical Risk Model with a Franchise and a Liability Limit; 4.1. Introduction; 4.2. Survival probability in the classical risk model with a franchise; 4.3. Survival probability in the classical risk model with a liability limit. | |
| 505 | 8 | |a 4.4. Survival probability in the classical risk model with both a franchise and a liability limitChapter 5. Optimal Control by the Franchise and Deductible Amounts in the Classical Risk Model; 5.1. Introduction; 5.2. Optimal control by the franchise amount; 5.3. Optimal control by the deductible amount; 5.4. Bibliographical notes; Chapter 6. Risk Models with Investments in Risk-Free and Risky Assets; 6.1. Description of the models; 6.2. Classical risk model with investments in risk-free and risky assets; 6.3. Risk model with stochastic premiums and investments in risk-free and risky assets. | |
| 505 | 8 | |a 6.4. Accuracy and reliability of uniform approximations of the survival probabilities by their statistical estimates6.5. Bibliographical notes; PART 2. SUPERMARTINGALE APPROACH TO THE ESTIMATION OF RUIN PROBABILITIES; Chapter 7. Risk Model with Variable Premium Intensity and Investments in One Risky Asset; 7.1. Description of the model; 7.2. Auxiliary results; 7.3. Existence and uniqueness theorem; 7.4. Supermartingale property for the exponential process; 7.5. Upper exponential bound for the ruin probability; 7.6. Bibliographical notes. | |
| 505 | 8 | |a Chapter 8. Risk Model with Variable Premium Intensity and Investments in One Risky Asset up to the Stopping Time of Investment Activity8.1. Description of the model; 8.2. Existence and uniqueness theorem; 8.3. Redefinition of the ruin time; 8.4. Supermartingale property for the exponential process; 8.5. Upper exponential bound for the ruin probability; 8.6. Exponentially distributed claim sizes; 8.7. Modification of the model; Chapter 9. Risk Model with Variable Premium Intensity and Investments in One Risk-Free and a Few Risky Assets; 9.1. Description of the model. | |
| 520 | |a Ruin Probabilities: Smoothness, Bounds, Supermartingale Approach deals with continuous-time risk models and covers several aspects of risk theory. The first of them is the smoothness of the survival probabilities. In particular, the book provides a detailed investigation of the continuity and differentiability of the infinite-horizon and finite-horizon survival probabilities for different risk models. Next, it gives some possible applications of the results concerning the smoothness of the survival probabilities. Additionally, the book introduces the supermartingale approach, which generalizes the martingale one introduced by Gerber, to get upper exponential bounds for the infinite-horizon ruin probabilities in some generalizations of the classical risk model with risky investments. | ||
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| 776 | 0 | 8 | |i Print version: |a Mishura, Yuliya. |t Ruin probabilities. |d [Place of publication not identified] : Elsevier, 2016 |z 1785482181 |z 9781785482182 |w (OCoLC)955540597 |
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