Ruin Probabilities

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. Olena Ragulina is Junior Researcher at the Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Ukraine Her research interests include actuarial and financial mathematics.

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