Ruin Probabilities. Smoothness, Bounds, Supermartingale Approach

Description

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. Content: Front matter,Copyright,PrefaceEntitled to full textPart 1: Smoothness of the Survival Probabilities with Applications1 - Classical Results on the Ruin Probabilities, Pages 3-26 2 - Classical Risk Model with Investments in a Risk-Free Asset, Pages 27-48 3 - Risk Model with Stochastic Premiums Investments in a Risk-Free Asset, Pages 49-64 4 - Classical Risk Model with a Franchise and a Liability Limit, Pages 65-104 5 - Optimal Control by the Franchise and Deductible Amounts in the Classical Risk Model, Pages 105-126 6 - Risk Models with Investments in Risk-Free and Risky Assets, Pages 127-162 7 - Risk Model with Variable Premium Intensity and Investments in One Risky Asset, Pages 165-185 8 - Risk Model with Variable Premium Intensity and Investments in One Risky Asset up to the Stopping Time of Investment Activity, Pages 187-203 9 - Risk Model with Variable Premium Intensity and Investments in One Risk-Free and a Few Risky Assets, Pages 205-229 Appendix - Mathematical Background, Pages 231-237 Bibliography, Pages 239-253 Abbreviations and Notation, Pages 255-257 Index, Pages 259-260