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 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 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 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 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 Asymptotic Behavior of Finite Time Ruin Probability in a By claim Risk Model with Constant Interest Rate written by Lei Wang and published by . This book was released on 2014 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Asymptotic Statistics in Insurance Risk Theory written by Yasutaka Shimizu and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book begins with the fundamental large sample theory, estimating ruin probability, and ends by dealing with the latest issues of estimating the Gerber-Shiu function. This book is the first to introduce the recent development of statistical methodologies in risk theory (ruin theory) as well as their mathematical validities. Asymptotic theory of parametric and nonparametric inference for the ruin-related quantities is discussed under the setting of not only classical compound Poisson risk processes (Cramér-Lundberg model) but also more general Lévy insurance risk processes. The recent development of risk theory can deal with many kinds of ruin-related quantities: the probability of ruin as well as Gerber-Shiu's discounted penalty function, both of which are useful in insurance risk management and in financial credit risk analysis. In those areas, the common stochastic models are used in the context of the structural approach of companies' default. So far, the probabilistic point of view has been the main concern for academic researchers. However, this book emphasizes the statistical point of view because identifying the risk model is always necessary and is crucial in the final step of practical risk management.
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 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 Asymptotics of Ruin Probabilities for Risk Processes Under Optimal Reinsurance Policies written by and published by . This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic ruin probabilities and optimal investment for an insurer written by Johanna Isabella Gaier and published by . This book was released on 2002 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Ruin Probabilities and Optimal Investment written by and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the infinite time ruin probability for an insurance company in the classical Cramér-Lundberg model with finite exponential moments. The additional non-classical feature is that the company is also allowed to invest in some stock market, modeled by geometric Brownian motion. We obtain an exact analogue of the classical estimate for the ruin probability without investment, i.e., an exponential inequality. The exponent is larger than the one obtained without investment, the classical Lundberg adjustment coefficient, and thus one gets a sharper bound on the ruin probability. A surprising result is that the trading strategy yielding the optimal asymptotic decay of the ruin probability simply consists in holding a fixed quantity (which can be explicitly calculated) in the risky asset, independent of the current reserve. This result is in apparent contradiction to the common believe that 'rich' companies should invest more in risky assets than 'poor' ones. The reason for this seemingly paradoxical result is that the minimization of the ruin probability is an extremely conservative optimization criterion, especially for 'rich' companies. (author's abstract).
Download or read book Asymptotic Tail Probabilities of Risk Processes in Insurance and Finance written by Xuemiao Hao and published by . This book was released on 2009 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finally, we consider the renewal risk model in which the surplus is invested into a portfolio consisting of both a riskless bond and a risky stock. The price process of the stock is modeled by an exponential Lévy process. We derive an asymptotic formula for the tail probability of the stochastically discounted net loss process.
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 Asymptotics of Ruin Probabilities for Risk Processes Under Optimal Reinsurance Policies written by and published by . This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
