Ruin Probabilities

Smoothness, Bounds, Supermartingale Approach

Inbunden, Engelska, 2016

Av Yuliya Mishura, Olena Ragulina, Ukraine) Mishura, Yuliya (Head, Department of Probability, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko Kyiv National University, Kiev, Ukraine) Ragulina, Olena (Taras Shevchenko National University of Kyiv

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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

Produktinformation

Utgivningsdatum2016-10-10
Mått152 x 229 x 0 mm
Vikt410 g
FormatInbunden
SpråkEngelska
Antal sidor276
FörlagElsevier Science
ISBN9781785482182

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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 Applications1: Classical Results on the Ruin Probabilities2: Classical Risk Model with Investments in a Risk-Free Asset3: Risk Model with Stochastic Premiums Investments in a Risk-Free Asset4: Classical Risk Model with a Franchise and a Liability Limit5: Optimal Control by the Franchise and Deductible Amounts in the Classical Risk Model6: Risk Models with Investments in Risk-Free and Risky AssetsPart 2: Supermartingale Approach to the Estimation of Ruin Probabilities7: Risk Model with Variable Premium Intensity and Investments in One Risky Asset8: Risk Model with Variable Premium Intensity and Investments in One Risky Asset up to the Stopping Time of Investment Activity9: Risk Model with Variable Premium Intensity and Investments in One Risk-Free and a Few Risky Assets