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

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