Ruin Probabilities

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.

Provides new original results
Detailed investigation of the continuity and differentiability of the infinite-horizon and finite-horizon survival probabilities, as well as possible applications of these results
An excellent supplement to current textbooks and monographs in risk theory
Contains a comprehensive list of useful references

Yuliya Mishura is Professor and Head of the Department of Probability Theory, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Ukraine. Her research interests include stochastic analysis, theory of stochastic processes, stochastic differential equations, numerical schemes, financial mathematics, risk processes, statistics of stochastic processes, and models with long-range dependence.

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.

• Provides new original results
• Detailed investigation of the continuity and differentiability of the infinite-horizon and finite-horizon survival probabilities, as well as possible applications of these results
• An excellent supplement to current textbooks and monographs in risk theory
• Contains a comprehensive list of useful references

Auteur

Yuliya Mishura is Professor and Head of the Department of Probability Theory, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Ukraine. Her research interests include stochastic analysis, theory of stochastic processes, stochastic differential equations, numerical schemes, financial mathematics, risk processes, statistics of stochastic processes, and models with long-range dependence.

Contenu

Part 1: Smoothness of the Survival Probabilities with Applications

1: Classical Results on the Ruin Probabilities

2: Classical Risk Model with Investments in a Risk-Free Asset

3: Risk Model with Stochastic Premiums Investments in a Risk-Free Asset

4: Classical Risk Model with a Franchise and a Liability Limit

5: Optimal Control by the Franchise and Deductible Amounts in the Classical Risk Model

6: Risk Models with Investments in Risk-Free and Risky Assets

Part 2: Supermartingale Approach to the Estimation of Ruin Probabilities

7: Risk Model with Variable Premium Intensity and Investments in One Risky Asset

8: Risk Model with Variable Premium Intensity and Investments in One Risky Asset up to the Stopping Time of Investment Activity

9: Risk Model with Variable Premium Intensity and Investments in One Risk-Free and a Few Risky Assets