Download or read book On the Probability of Maximum Severity of Ruin for a Classical and Renewal Risk Model written by Palash Ranjan Das and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Ruin Probabilities written by S?ren Asmussen and published by World Scientific. This book was released on 2000 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text is a treatment of classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramer-Lundberg approximation, exact solutions, other approximations (for example, 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 or periodicity. Special features of the book are the emphasis on change of measure techniques, phase-type distributions as computational vehicle and the connection to other applied probability areas like queueing theory.
Download or read book Renewal Risk Processes with Stochastic Returns on Investments written by Corina D. Constantinescu and published by . This book was released on 2006 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis considers one of the classical problems in the actuarial mathematics literature, the decay of the probability of ruin in the collective risk model. The claim number process N(t) is assumed to be a renewal process, the resulting model being referred as the Sparre Andersen risk model. The inter-claim times form a sequence of independent identically distributed random variables. The additional non-classical feature is that the company invests in an asset with stochastic returns. A very general integro-differential equation is derived for expected values of functions of this renewal risk model with stochastic returns. Moreover, as a particular case, an integro-differential equation is derived for the probability of ruin, under very general conditions regarding the claim sizes, claim arrivals and the returns from investment. Through this unified approach, specific integro-differential equations of the ruin probability may be written for various risk model scenarios, allowing the asymptotic analysis of the ruin probabilities.
Download or read book On the Evaluation of Finite Time Ruin Probabilities in a Dependent Risk Model written by Dimitrina Dimitrova and published by . This book was released on 2014 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper establishes some enlightening connections between the explicit formulas of the finite-time ruin probability established by Ignatov and Kaishev (2000, 2004) and Ignatov et al. (2001) for a risk model allowing dependence. The numerical properties of these formulas are investigated and efficient algorithms for computing ruin probability with prescribed accuracy are presented. Extensive numerical comparisons and examples are provided.Research on ruin probability beyond the classical risk model has intensified in recent years. More general ruin probability models assuming dependence between claim amounts and/or claim arrivals and non-linear aggregate premium income have been considered in the actuarial and applied probability literature. Such models are better suited to reflect the dependence in the arrival and severity of losses generated by portfolios of insurance policies. Exploring ruin probability theoretically and numerically, under these more general dependence assumptions, is of utmost importance within the Solvency II framework of internal insolvency-risk model building.
Download or read book Ruin Probabilities written by S?ren Asmussen and published by World Scientific. This book was released on 2010 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramr?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.
Download or read book Characteristics of Ruin Probabilities in Classical Risk Models with and Without Investment Cox Risk Models and Perturbed Risk Models written by Hanspeter Schmidli and published by . This book was released on 2000 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Surplus Analysis of Sparre Andersen Insurance Risk Processes written by Gordon E. Willmot and published by Springer. This book was released on 2017-12-21 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This carefully written monograph covers the Sparre Andersen process in an actuarial context using the renewal process as the model for claim counts. A unified reference on Sparre Andersen (renewal risk) processes is included, often missing from existing literature. The authors explore recent results and analyse various risk theoretic quantities associated with the event of ruin, including the time of ruin and the deficit of ruin. Particular attention is given to the explicit identification of defective renewal equation components, which are needed to analyse various risk theoretic quantities and are also relevant in other subject areas of applied probability such as dams and storage processes, as well as queuing theory. Aimed at researchers interested in risk/ruin theory and related areas, this work will also appeal to graduate students in classical and modern risk theory and Gerber-Shiu analysis.
Download or read book On the Time Value of Ruin for Insurance Risk Models written by Shuanming Li and published by . This book was released on 2004 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Maximum Surplus Before Ruin for Dependent Risk Models Through Farlie Gumbel Morgenstern Copula written by Wuyuan Jiang and published by . This book was released on 2014 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: We extend the classical compound Poisson risk model to consider the distribution of the maximum surplus before ruin where the claim sizes depend on inter-claim times via the Farlie-Gumbel-Morgenstern copula. We derive an integro-differential equation with certain boundary conditions for this distribution, of which the Laplace transform is provided. We obtain the renewal equation and explicit expressions for this distribution are derived when the claim amounts are exponentially distributed. Finally, we present numerical examples.
Download or read book Ruin Probabilities written by Yuliya Mishura and published by Elsevier. This book was released on 2016-11-08 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book The Distribution of the Time to Ruin in the Classical Risk Model written by David C. M. Dickson and published by . This book was released on 2002 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book ASTIN Bulletin written by and published by . This book was released on 2008 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ruin Probabilities 2nd Edition written by Soren Asmussen and published by World Scientific Publishing Company. This book was released on 2010-09-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-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.
Download or read book Ruin Theory Under a Threshold Insurance Risk Model written by Kwok-Man Kwan and published by . This book was released on 2017-01-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book A Revisit to Asymptotic Ruin Probabilities for a Bidimensional Renewal Risk Model written by Jinzhu Li and published by . This book was released on 2017 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently, Yang and Li (2014, Insurance: Mathematics and Economics) studied a bidimensional renewal risk model with constant force of interest and dependent subexponential claims. Under the special Farlie-Gumbel-Morgenstern dependence structure and a technical moment condition on the claim-number process, they derived an asymptotic expansion for the finite-time ruin probability. In this paper, we show that their result can be extended to a much more general dependence structure without any extra condition on the renewal claim-number process. We also give some asymptotic expansions for the corresponding infinite-time ruin probability within the scope of extended regular variation.
Download or read book Topics in Delayed Renewal Risk Models written by So-Yeun Kim and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Note on the Convexity of Ruin Probabilities written by David Landriault and published by . This book was released on 2017 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conditions for the convexity of compound geometric tails and compound geometric convolution tails are established. The results are then applied to analyze the convexity of the ruin probability and the Laplace transform of the time to ruin in the classical compound Poisson risk model with and without diffusion. An application to an optimization problem is given.
