Cargando…
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.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.
- 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.
- 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.
- 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.
- 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.