Author: Shuanming Li
Publisher:
ISBN:
Category : Risk (Insurance)
Languages : en
Pages : 366

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Book Description

Author: David C. M. Dickson
Publisher: Cambridge University Press
ISBN: 1316839532
Category : Business & Economics
Languages : en
Pages : 307

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Book Description
The focus of this book is on the two major areas of risk theory: aggregate claims distributions and ruin theory. For aggregate claims distributions, detailed descriptions are given of recursive techniques that can be used in the individual and collective risk models. For the collective model, the book discusses different classes of counting distribution, and presents recursion schemes for probability functions and moments. For the individual model, the book illustrates the three most commonly applied techniques. Beyond the classical topics in ruin theory, this new edition features an expanded section covering time of ruin problems, Gerber–Shiu functions, and the application of De Vylder approximations. Suitable for a first course in insurance risk theory and extensively classroom tested, the book is accessible to readers with a solid understanding of basic probability. Numerous worked examples are included and each chapter concludes with exercises for which complete solutions are provided.

Author: S?ren Asmussen
Publisher: World Scientific
ISBN: 9814282529
Category : Mathematics
Languages : en
Pages : 621

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Book Description
The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cram‚r?Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber?Shiu functions and dependence.

Author: Kwok-Man Kwan
Publisher:
ISBN: 9781374672857
Category :
Languages : en
Pages :

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Book Description
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

Author: Palash Ranjan Das
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Book Description
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.

Author: Yuliya Mishura
Publisher: Elsevier
ISBN: 0081020988
Category : Mathematics
Languages : en
Pages : 278

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Book 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. 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

Author: Shu Li
Publisher:
ISBN:
Category :
Languages : en
Pages : 142

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Book Description
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.

Author: Jingchao Li
Publisher:
ISBN:
Category : Insurance
Languages : en
Pages : 235

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Book Description

Author: David C. M. Dickson
Publisher: Cambridge University Press
ISBN: 110715460X
Category : Business & Economics
Languages : en
Pages : 307

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

Author: Ricardas Zitikis
Publisher: MDPI
ISBN: 3039285165
Category : Business & Economics
Languages : en
Pages : 210

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Book Description
Developing techniques for assessing various risks and calculating probabilities of ruin and survival are exciting topics for mathematically-inclined academics. For practicing actuaries and financial engineers, the resulting insights have provided enormous opportunities but also created serious challenges to overcome, thus facilitating closer cooperation between industries and academic institutions. In this book, several renown researchers with extensive interdisciplinary research experiences share their thoughts that, in one way or another, contribute to the betterment of practice and theory of decision making under uncertainty. Behavioral, cultural, mathematical, and statistical aspects of risk assessment and modelling have been explored, and have been often illustrated using real and simulated data. Topics range from financial and insurance risks to security-type risks, from one-dimensional to multi- and even infinite-dimensional risks. The articles in the book were written with a broad audience in mind and should provide enjoyable reading for those with university level degrees and/or those who have studied for accreditation by various actuarial and financial societies.