Ruin Theory Under A Threshold Insurance Risk Model

DOWNLOAD

Download Ruin Theory Under A Threshold Insurance Risk Model PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Ruin Theory Under A Threshold Insurance Risk Model book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Ruin Theory Under A Threshold Insurance Risk Model

DOWNLOAD
Author : Kwok-man Kwan
language : en
Publisher:
Release Date : 2007

Ruin Theory Under A Threshold Insurance Risk Model written by Kwok-man Kwan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Probabilities categories.

Ruin Theory Under A Threshold Insurance Risk Model

DOWNLOAD
Author : Kwok-Man Kwan
language : en
Publisher:
Release Date : 2017-01-27

Ruin Theory Under A Threshold Insurance Risk Model written by Kwok-Man Kwan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-27 with categories.

This dissertation, "Ruin Theory Under a Threshold Insurance Risk Model" by Kwok-man, Kwan, 關國文, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of the thesis entitled RUIN THEORY UNDER A THRESHOLD INSURANCE RISK MODEL submitted by Kwan, Kwok Man for the degree of Master of Philosophy at The University of Hong Kong in April 2007 Since the classical Lundberg model was studied in 1903, there have been many studies about the generalization of the classical insurance risk model. The most popular ones are the Sparre-Anderson model, the Markov-modulated model and the di(R)usion-perturbed model. Recently, more and more attentions have been paid to the dependent models. The risk models with dependent claim sizes and the common shock models with di(R)erent lines of business have been studied by many authors. This thesis studies two risk models with dependence between claim size and inter-arrivaltimethroughathresholdstructure.Intherstinsuranceriskmodel, the distribution of the inter-arrival time depends on the last claim size: when the lastclaimsizeisbelowathreshold, thecurrentinter-arrivaltimefollowsacertain probability distribution; otherwise, it follows another probability distribution. Inthe second insurance risk model, its dependence relation is the reversal of the previous one, that is: when the last inter-arrival time is below a threshold, the current claim size follows a certain probability distribution; otherwise, it follows another probability distribution. It was found that the ruin probability became a dicult problem when the model involved these dependent structures. In order to obtain the solution of the ultimate ruin probability for these de- pendent models, the integro-di(R)erential equation, the integral equation and the Laplace transform satised by the ruin probability were derived and the explicit formula of the ruin probability was obtained in the case of exponential claim size. DOI: 10.5353/th_b3832003 Subjects: Risk (Insurance) - Mathematical models Probabilities

Adaptive Policies And Drawdown Problems In Insurance Risk Models

DOWNLOAD
Author : Shu Li
language : en
Publisher:
Release Date : 2015

Adaptive Policies And Drawdown Problems In Insurance Risk Models written by Shu Li and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.

Ruin theory studies an insurer's solvency risk, and to quantify such a risk, a stochastic process is used to model the insurer's surplus process. In fact, research on ruin theory dates back to the pioneer works of Lundberg (1903) and Cramer (1930), where the classical compound Poisson risk model (also known as the Cramer-Lundberg model) was first introduced. The research was later extended to the Sparre Andersen risk model, the Markov arrival risk model, the Levy insurance risk model, and so on. However, in most analysis of the risk models, it is assumed that the premium rate per unit time is constant, which does not always reflect accurately the insurance environment. To better reflect the surplus cash flows of an insurance portfolio, there have been some studies (such as those related to dividend strategies and tax models) which allow the premium rate to take different values over time. Recently, Landriault et al. (2012) proposed the idea of an adaptive premium policy where the premium rate charged is based on the behaviour of the surplus process itself. Motivated by their model, the first part of the thesis focuses on risk models including certain adjustments to the premium rate to reflect the recent claim experience. In Chapter 2, we generalize the Gerber-Shiu analysis of the adaptive premium policy model of Landriault et al. (2012). Chapter 3 proposes an experience-based premium policy under the compound Poisson dynamic, where the premium rate changes are based on the increment between successive random review times. In Chapter 4, we examine a drawdown-based regime-switching Levy insurance model, where the drawdown process is used to model an insurer's level of financial distress over time, and to trigger regime-switching (or premium changes). Similarly to ruin problems which examine the first passage time of the risk process below a threshold level, drawdown problems relate to the first time that a drop in value from a historical peak exceeds a certain level (or equivalently the first passage time of the reflected process above a certain level). As such, drawdowns are fundamentally relevant from the viewpoint of risk management as they are known to be useful to detect, measure and manage extreme risks. They have various applications in many research areas, for instance, mathematical finance, applied probability and statistics. Among the common insurance surplus processes in ruin theory, drawdown episodes have been extensively studied in the class of spectrally negative Levy processes, or more recently, its Markov additive generalization. However, far less attention has been paid to the Sparre Andersen risk model, where the claim arrival process is modelled by a renewal process. The difficulty lies in the fact that such a process does not possess the strong Markov property. Therefore, in the second part of the thesis (Chapter 5), we extend the two-sided exit and drawdown analyses to a renewal risk process. In conclusion, the general focus of this thesis is to derive and analyze ruin-related and drawdown-related quantities in insurance risk models with adaptive policies, and assess their risk management impacts. Chapter 6 ends the thesis by some concluding remarks and directions for future research.

Insurance Risk And Ruin

DOWNLOAD
Author : David C. M. Dickson
language : en
Publisher: Cambridge University Press
Release Date : 2016-10-27

Insurance Risk And Ruin written by David C. M. Dickson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-27 with Business & Economics categories.

Balancing rigor and intuition, the new edition of this first course in risk theory has added exercises and expands on contemporary topics.

Analysis Of Some Risk Processes In Ruin Theory

DOWNLOAD
Author : Luyin Liu
language : en
Publisher:
Release Date : 2017-01-26

Analysis Of Some Risk Processes In Ruin Theory written by Luyin Liu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-26 with categories.

This dissertation, "Analysis of Some Risk Processes in Ruin Theory" by Luyin, Liu, 劉綠茵, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: In the literature of ruin theory, there have been extensive studies trying to generalize the classical insurance risk model. In this thesis, we look into two particular risk processes considering multi-dimensional risk and dependent structures respectively. The first one is a bivariate risk process with a dividend barrier, which concerns a two-dimensional risk model under a barrier strategy. Copula is used to represent the dependence between two business lines when a common shock strikes. By defining the time of ruin to be the first time that either of the two lines has its surplus level below zero, we derive a discrete approximation procedure to calculate the expected discounted dividends until ruin under such a model. A thorough discussion of application in proportional reinsurance with numerical examples is provided as well as an examination of the joint optimal dividend barrier for the bivariate process. The second risk process is a semi-Markovian dual risk process. Assuming that the dependence among innovations and waiting times is driven by a Markov chain, we analyze a quantity resembling the Gerber-Shiu expected discounted penalty function that incorporates random variables defined before and after the time of ruin, such as the minimum surplus level before ruin and the time of the first gain after ruin. General properties of the function are studied, and some exact results are derived upon distributional assumptions on either the inter-arrival times or the gain amounts. Applications in a perpetual insurance and the last inter-arrival time before ruin are given along with some numerical examples. DOI: 10.5353/th_b5153734 Subjects: Risk (Insurance) - Mathematical models

Risk Theory

DOWNLOAD
Author : Hanspeter Schmidli
language : en
Publisher: Springer
Release Date : 2018-04-04

Risk Theory written by Hanspeter Schmidli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-04 with Business & Economics categories.

This book provides an overview of classical actuarial techniques, including material that is not readily accessible elsewhere such as the Ammeter risk model and the Markov-modulated risk model. Other topics covered include utility theory, credibility theory, claims reserving and ruin theory. The author treats both theoretical and practical aspects and also discusses links to Solvency II. Written by one of the leading experts in the field, these lecture notes serve as a valuable introduction to some of the most frequently used methods in non-life insurance. They will be of particular interest to graduate students, researchers and practitioners in insurance, finance and risk management.

Ruin Theory For Portfolio Risk Modeling In Banking And Insurance

DOWNLOAD
Author : Guusje Delsing
language : en
Publisher:
Release Date : 2022

Ruin Theory For Portfolio Risk Modeling In Banking And Insurance written by Guusje Delsing and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.

Gerber Shiu Risk Theory

DOWNLOAD
Author : Andreas E. Kyprianou
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-02

Gerber Shiu Risk Theory written by Andreas E. Kyprianou and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-02 with Mathematics categories.

Motivated by the many and long-standing contributions of H. Gerber and E. Shiu, this book gives a modern perspective on the problem of ruin for the classical Cramér–Lundberg model and the surplus of an insurance company. The book studies martingales and path decompositions, which are the main tools used in analysing the distribution of the time of ruin, the wealth prior to ruin and the deficit at ruin. Recent developments in exotic ruin theory are also considered. In particular, by making dividend or tax payments out of the surplus process, the effect on ruin is explored. Gerber-Shiu Risk Theory can be used as lecture notes and is suitable for a graduate course. Each chapter corresponds to approximately two hours of lectures.

On The Probability Of Maximum Severity Of Ruin For A Classical And Renewal Risk Model

DOWNLOAD
Author : Palash Ranjan Das
language : en
Publisher:
Release Date : 2016

On The Probability Of Maximum Severity Of Ruin For A Classical And Renewal Risk Model written by Palash Ranjan Das and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.

The authors of this paper engage ruin theory as a mathematical basis for quantifying the financial risks in insurance industry. Considering a classical risk model with dividend barrier it is calibrated to obtain the maximum probability of ruin when the claim amount distribution is either exponential or Erlangian. It is to be noted that for numerical evaluation, the premium loading factor is taken to be 20% in both the cases. In order to ensure fair comparison, exponential and Erlangian parameters have been chosen in such a way that their mean and the expected total claims are same for both the distributions over a given time interval. Ultimately, it is generalized that the classical risk model by considering a renewal risk model can be used to find an expression for the maximum severity of ruin in the insurance industry.

Gerber Shiu Risk Theory

DOWNLOAD
Author : Andreas Kyprianou
language : en
Publisher: Springer
Release Date : 2013-11-27

Gerber Shiu Risk Theory written by Andreas Kyprianou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.

Motivated by the many and long-standing contributions of H. Gerber and E. Shiu, this book gives a modern perspective on the problem of ruin for the classical Cramér–Lundberg model and the surplus of an insurance company. The book studies martingales and path decompositions, which are the main tools used in analysing the distribution of the time of ruin, the wealth prior to ruin and the deficit at ruin. Recent developments in exotic ruin theory are also considered. In particular, by making dividend or tax payments out of the surplus process, the effect on ruin is explored. Gerber-Shiu Risk Theory can be used as lecture notes and is suitable for a graduate course. Each chapter corresponds to approximately two hours of lectures.