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Author: Palash Ranjan Das Publisher: ISBN: Category : Languages : en Pages :
Book Description
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.
Author: Palash Ranjan Das Publisher: ISBN: Category : Languages : en Pages :
Book Description
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.
Author: Palash Ranjan Das Publisher: ISBN: Category : Languages : en Pages :
Book Description
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.
Author: S?ren Asmussen Publisher: World Scientific ISBN: 9814282529 Category : Mathematics Languages : en Pages : 621
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: Palash Ranjan Das Publisher: ISBN: Category : Languages : en Pages :
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: T. L. Lai Publisher: ISBN: Category : Mathematics Languages : en Pages : 560
Book Description
Presents a collection of 18 papers, many of which are surveys, on asymptotic theory in probability and statistics, with applications to a variety of problems. This volume comprises three parts: limit theorems, statistics and applications, and mathematical finance and insurance. It is suitable for graduate students in probability and statistics.
Author: Rongbo Zhu Publisher: Springer Science & Business Media ISBN: 3642163351 Category : Computers Languages : en Pages : 552
Book Description
This book constitutes the proceedings of the International Conference on Information Computing and Applications, held in Tangshan, China, in October 2010.
Author: Dimitrios George Konstantinides Publisher: World Scientific Publishing Company ISBN: 9789813223141 Category : Mathematics Languages : en Pages : 494
Book Description
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
Author: Publisher: John Wiley & Sons ISBN: 0470035498 Category : Mathematics Languages : en Pages : 2163
Book Description
Leading the way in this field, the Encyclopedia of Quantitative Risk Analysis and Assessment is the first publication to offer a modern, comprehensive and in-depth resource to the huge variety of disciplines involved. A truly international work, its coverage ranges across risk issues pertinent to life scientists, engineers, policy makers, healthcare professionals, the finance industry, the military and practising statisticians. Drawing on the expertise of world-renowned authors and editors in this field this title provides up-to-date material on drug safety, investment theory, public policy applications, transportation safety, public perception of risk, epidemiological risk, national defence and security, critical infrastructure, and program management. This major publication is easily accessible for all those involved in the field of risk assessment and analysis. For ease-of-use it is available in print and online.
Author: Jinzhu Li Publisher: ISBN: Category : Languages : en Pages : 15
Book Description
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.
Author: Palash Ranjan Das
Author: Palash Ranjan Das
Author: Palash Ranjan Das
Author: S?ren Asmussen
Author: So-Yeun Kim
Author: Palash Ranjan Das
Author: T. L. Lai
Author: Rongbo Zhu
Author: Dimitrios George Konstantinides
Author: 
Author: Jinzhu Li