Overview

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.

Full Product Details

Author:   Yuliya Mishura (Head, Department of Probability, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko Kyiv National University, Kiev, Ukraine) ,  Olena Ragulina (Taras Shevchenko National University of Kyiv, Ukraine)
Publisher:   ISTE Press Ltd - Elsevier Inc
Imprint:   ISTE Press Ltd - Elsevier Inc
Dimensions:   Width: 15.20cm , Height: 1.90cm , Length: 22.90cm
Weight:   0.410kg
ISBN:  

9781785482182

ISBN 10:   1785482181
Pages:   276
Publication Date:   10 October 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

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

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Author Information

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.

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