Topics in a Delay Renewal Risk Model Perturbed by Diffusion Process with Dependence Between Claim Sizes and Inter-occurrence Times PDF Download

Author: Essodina Takouda
Publisher:
ISBN:
Category : Actuarial science
Languages : en
Pages : 0

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Author: So-Yeun Kim
Publisher:
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Category :
Languages : en
Pages :

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Author: Kokou Essiomle
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Category : Probabilities
Languages : en
Pages : 0

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Author: Jinzhu Li
Publisher:
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Category :
Languages : en
Pages : 15

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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: Lai-Mei Wan
Publisher: Open Dissertation Press
ISBN: 9781374730465
Category : Mathematics
Languages : en
Pages : 80

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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

Author: Wuyuan Jiang
Publisher:
ISBN:
Category :
Languages : en
Pages : 20

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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.

Author: Luyin Liu
Publisher:
ISBN: 9781361330791
Category :
Languages : en
Pages :

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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

Author: Palash Ranjan Das
Publisher:
ISBN:
Category :
Languages : en
Pages :

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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: Wei Zhu
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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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.

Author: Yichun Chi
Publisher:
ISBN:
Category :
Languages : en
Pages : 31

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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.