Download or read book Topics in a Delay Renewal Risk Model Perturbed by Diffusion Process with Dependence Between Claim Sizes and Inter occurrence Times written by Essodina Takouda and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Ruin Probabilities and Related Quantities in the Renewal Risk Model with Dependence and Time Delay in Claims Settlement written by Kokou Essiomle and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 RUIN ANALYSIS OF CORRELATED AG written by Lai-Mei Wan and published by Open Dissertation Press. This book was released on 2017-01-27 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "Ruin Analysis of Correlated Aggregate Claims Models" by Lai-mei, Wan, 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 thesis entitled RUIN ANALYSIS OF CORRELATED AGGREGATE CLAIMS MODELS Submitted by WAN LAI MEI for the degree of Master of Philosophy at The University of Hong Kong in January 2005 In recent years, study of risk models with dependent classes of insurance business has become a popular topic in actuarial science. The main theme of this the- sis is to explore more general models which include various types of dependence structures among classes in a book of insurance business. Specifically, ruin anal- ysis was performed on two correlated aggregate claims models for a book of m (m>= 2) dependent classes of insurance business. Firstly, a discrete-time risk model was considered with m dependent classes of business in which a time-series approach was adopted. The claim processes of the m classes were assumed to follow a multivariate autoregressive time-series model of order 1. In this framework, different classes were dependent due to the time-series structure and the correlation among current claims. The probability of ruin for the risk model was studied. In the case of m = 2, simulation studiesfor absolutely continuous bivariate exponential (ACBVE) claim distribution and bivariate gamma claim distribution were performed. Next, a continuous-time risk model with m dependent classes of insurance business was investigated. The claim-number processes of the m classes were correlated due to the so-called thinning dependence together with a common shock. Various aspects of the proposed model were examined, and the impact of therelationofdependenceviatheadjustmentcoefficientwasthenstudied. Inthe bivariate case (m = 2), a numerical study was performed for exponential claim distribution and simulation studies were carried out for non-exponential claim distributions. DOI: 10.5353/th_b3070570 Subjects: Risk (Insurance) Probabilities Insurance claims - Mathematical models Insurance - Mathematics
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 Analysis of Some Risk Processes in Ruin Theory written by Luyin Liu and published by . This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Barrier Probability in a Renewal Risk Model written by Palash Ranjan Das and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers a renewal risk model with dividend barrier for which the claim inter-arrival time is Erlang(2) distributed. The purpose is to derive explicit expression for the barrier probability, that is, the probability of absorption by an upper barrier 'b', before ruin occurs. To obtain analytical results concerning this barrier probability, the claim amount distributions are considered to be either exponential or Erlang(2). Thus in the process, the paper extends the results obtained by Das and Chakrabarti (2017) for a classical risk model to a more general renewal risk model.
Download or read book A Risk Model with Delayed Claims written by Angelos Dassios and published by . This book was released on 2015 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we introduce a simple risk model with delayed claims, an extension of the classical Poisson model. The arrival of claims is assumed to be a Poisson process, claims follow a light-tailed distribution, and each loss payment of the claims will be settled with a random period of delay. We obtain asymptotic expressions for the ruin probability by exploiting a connection to Poisson models that are not time-homogeneous. A finer asymptotic formula is obtained for the special case of exponentially delayed claims and an exact formula when the claims are also exponentially distributed.
Download or read book Ruin Probabilities in an Erlang Risk Model with Dependence Structure Based on an Independent Gamma Distributed Time Window written by Wei Zhu and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we investigate an Erlang risk model wherein the premium rate and claim size distribution are dynamically adjusted based on the inter-arrival time and an independent random time window. The ruin probabilities within this model adhere to a system of fractional integro-differential equations. For a specific class of claim size distributions, this system can be further transformed into a fractional differential equation system. We provide explicit solutions for these fractional boundary problems and illustrate our findings with several numerical examples.
Download or read book An Insurance Risk Model with Stochastic Volatility written by Yichun Chi and published by . This book was released on 2010 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we extend the Cramer-Lundberg insurance risk model perturbed by diffusion to incorporate stochastic volatility and study the resulting Gerber-Shiu expected discounted penalty (EDP) function. Under the assumption that volatility is driven by an underlying Ornstein-Uhlenbeck (OU) process, we derive the integro-differential equation which the EDP function satisfies. Not surprisingly, no closed-form solution exists; however, assuming the driving OU process is fast mean-reverting, we apply singular perturbation theory to obtain an asymptotic expansion of the solution. Two integro-differential equations for the first two terms in this expansion are obtained and explicitly solved. When the claim size distribution is of phase-type, the asymptotic results simplify even further and we succeed in estimating the error of the approximation. Hyper-exponential and mixed-Erlang distributed claims are considered in some detail.
Download or read book Uncertain Renewal Processes written by Kai Yao and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores various renewal processes in the context of probability theory, uncertainty theory and chance theory. It also covers the applications of these renewal processes in maintenance models and insurance risk models. The methods used to derive the limit of the renewal rate, the reward rate, and the availability rate are of particular interest, as they can easily be extended to the derivation of other models. Its comprehensive and systematic treatment of renewal processes, renewal reward processes and the alternating renewal process is one of the book's major features, making it particularly valuable for readers who are interested in learning about renewal theory. Given its scope, the book will benefit researchers, engineers, and graduate students in the fields of mathematics, information science, operations research, industrial engineering, etc.
Download or read book On the Discounted Penalty Function in a Discrete Time Renewal Risk Model with General Interclaim Times written by Xueyuan Wu and published by . This book was released on 2007 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bulletin of the Atomic Scientists written by and published by . This book was released on 1970-12 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Bulletin of the Atomic Scientists is the premier public resource on scientific and technological developments that impact global security. Founded by Manhattan Project Scientists, the Bulletin's iconic "Doomsday Clock" stimulates solutions for a safer world.
Download or read book Lectures on the Poisson Process written by Günter Last and published by Cambridge University Press. This book was released on 2017-10-26 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.
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 Stochastic Processes for Insurance and Finance written by Tomasz Rolski and published by Wiley. This book was released on 2009-03-09 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Wiley Paperback Series makes valuable content more accessible to a new generation of statisticians, mathematicians and scientists. Stochastic Processes for Insurance and Finance offers a thorough yet accessible reference for researchers and practitioners of insurance mathematics. Building on recent and rapid developments in applied probability the authors describe in general terms models based on Markov processes, martingales and various types of point processes. Discussing frequently asked insurance questions, the authors present a coherent overview of this subject and specifically address: the principle concepts of insurance and finance practical examples with real life data numerical and algorithmic procedures essential for modern insurance practices Assuming competence in probability calculus, this book will provide a rigorous treatment of insurance risk theory recommended for researchers and students interested in applied probability as well as practitioners of actuarial sciences. “An excellent text” Australian & New Zealand Journal of Statistics
