Download or read book Some Aspects of the Barrier Probability in a Classical Risk Model written by Palash Ranjan Das and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we have considered a classical risk model with dividend barrier, in which claim inter-occurrence times are exponentially distributed. Our aim is to obtain explicit expression for the barrier probability B(u, b), the upper barrier being assumed to be 'b', before ruin occurs when the claim amount distribution is either exponential or erlangian. It is to be noted that the premium loading factor is taken to be 20% in both the cases. In order to ensure fair comparison, we have chosen the exponential and erlangian parameters in such a way that their mean and hence the expected total claims are same for both the distributions over a given time interval. Ultimately, through numerical evaluation of the barrier probability for both the claim amount distributions, we investigate whether there is any significant difference between the two.
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 Aspects of Risk Theory written by Jan Grandell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Risk theory, which deals with stochastic models of an insurance business, is a classical application of probability theory. The fundamental problem in risk theory is to investigate the ruin possibility of the risk business. Traditionally the occurrence of the claims is described by a Poisson process and the cost of the claims by a sequence of random variables. This book is a treatise of risk theory with emphasis on models where the occurrence of the claims is described by more general point processes than the Poisson process, such as renewal processes, Cox processes and general stationary point processes. In the Cox case the possibility of risk fluctuation is explicitly taken into account. The presentation is based on modern probabilistic methods rather than on analytic methods. The theory is accompanied with discussions on practical evaluation of ruin probabilities and statistical estimation. Many numerical illustrations of the results are given.
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 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 Ruin Probabilities 2nd Edition written by Soren Asmussen and published by World Scientific. This book was released on 2010-09-09 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 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 Insurance Risk and Ruin written by David C. M. Dickson and published by Cambridge University Press. This book was released on 2016-10-27 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Balancing rigor and intuition, the new edition of this first course in risk theory has added exercises and expands on contemporary topics.
Download or read book Risk Theory A Heavy Tail Approach written by Dimitrios George Konstantinides and published by #N/A. This book was released on 2017-07-07 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Heavy-tailed risk modelling plays a central role in modern risk theory; within this perspective, the book provides an excellent guide concerning problems and solutions in risk theory.'zbMATHThis book is written to help graduate students and young researchers to enter quickly into the subject of Risk Theory. It can also be used by actuaries and financial practitioners for the optimization of their decisions and further by regulatory authorities for the stabilization of the insurance industry. The topic of extreme claims is especially presented as a crucial feature of the modern ruin probability.
Download or read book Stochastic Optimization in Insurance written by Pablo Azcue and published by Springer. This book was released on 2014-06-19 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of the book is to show how a viscosity approach can be used to tackle control problems in insurance. The problems covered are the maximization of survival probability as well as the maximization of dividends in the classical collective risk model. The authors consider the possibility of controlling the risk process by reinsurance as well as by investments. They show that optimal value functions are characterized as either the unique or the smallest viscosity solution of the associated Hamilton-Jacobi-Bellman equation; they also study the structure of the optimal strategies and show how to find them. The viscosity approach was widely used in control problems related to mathematical finance but until quite recently it was not used to solve control problems related to actuarial mathematical science. This book is designed to familiarize the reader on how to use this approach. The intended audience is graduate students as well as researchers in this area.
Download or read book Practical Risk Theory for Actuaries written by C.D. Daykin and published by CRC Press. This book was released on 1993-12-01 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic textbook covers all aspects of risk theory in a practical way. It builds on from the late R.E. Beard's extremely popular book Risk Theory, but features more emphasis on simulation and modeling and on the use of risk theory as a practical tool. Practical Risk Theory is a textbook for practicing and student actuaries on the practical aspects of stochastic modeling of the insurance business. It has its roots in the classical theory of risk but introduces many new elements that are important in managing the insurance business but are usually ignored in the classical theory. The authors avoid overcomplicated mathematics and provide an abundance of diagrams.
Download or read book Study on the Dual Risk Model with Time Correlated Income and Dividend Barrier written by Ran Xu and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is dedicated to study the discrete time compound binomial dual risk model, where the income is time-correlated, and there is a constant dividend barrier. It is close to the reality if we consider that the incomes in different periods are correlated. And in this paper, the income is assumed to follow a compound binomial process, each time there is a income ( main-income), there will be a by-income; but the by-income could delay to next period for some certain probability. Under this time-correlated scenario, the relationship between the dual model and the classical risk model is studied and some important probabilities for the dual model are derived. The differential equations satisfied by the expected dividend payouts until ruin are derived, some explicit results are obtained under some specific assumptions.
Download or read book Memoirs written by Hanspeter Schmidli and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Risk Theory written by Dimitrios George Konstantinides and published by World Scientific Publishing Company. This book was released on 2017-07-10 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preface -- Classical risk model -- Renewal risk model -- Ruin probability estimation -- Extreme value theory -- Regular variation -- Ruin under subexponentiality -- Random sums -- The single big jump -- Ruin under constant interest force -- Absolute ruin -- Discrete dependence model -- Ruin under dependence -- Multivariate regular variation -- Bibliography -- Index
Download or read book Modern Problems of Stochastic Analysis and Statistics written by Vladimir Panov and published by Springer. This book was released on 2017-11-21 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together the latest findings in the area of stochastic analysis and statistics. The individual chapters cover a wide range of topics from limit theorems, Markov processes, nonparametric methods, acturial science, population dynamics, and many others. The volume is dedicated to Valentin Konakov, head of the International Laboratory of Stochastic Analysis and its Applications on the occasion of his 70th birthday. Contributions were prepared by the participants of the international conference of the international conference “Modern problems of stochastic analysis and statistics”, held at the Higher School of Economics in Moscow from May 29 - June 2, 2016. It offers a valuable reference resource for researchers and graduate students interested in modern stochastics.
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 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 Information Computing and Applications written by Baoxiang Liu and published by Springer. This book was released on 2011-12-08 with total page 793 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Second International Conference on Information Computing and Applications, ICICA 2010, held in Qinhuangdao, China, in October 2011. The 97 papers presented were carefully reviewed and selected from numerous submissions. They are organized in topical sections on computational economics and finance, computational statistics, mobile computing and applications, social networking and computing, intelligent computing and applications, internet and Web computing, paralelle and distributed computing, and system simulation and computing.
