Description
Ruin Probabilities
Smoothness, Bounds, Supermartingale Approach
Authors: Mishura Yuliya, Ragulina Olena
Language: EnglishKeywords
continuous-time risk model; classical risk model; risk model with stochastic premiums; risk model with investments; risk-free asset; risky asset; infinite-horizon survival probability; finite-horizon survival probability; infinite-horizon ruin probability; continuity; differentiability; (partial) integro-differential equation; Hamilton-Jacobi-Bellman equation; stochastic differential equation; exponential bound; power bound; analytic expression; optimal control problem; franchise; deductible; liability limit; verification theorem; existence and uniqueness theorem; uniform approximation
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Description
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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
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.
- 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