• Title, Summary, Keyword: the ruin probability

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A NOTE ON THE SEVERITY OF RUIN IN THE RENEWAL MODEL WITH CLAIMS OF DOMINATED VARIATION

  • Tang, Qihe
    • Bulletin of the Korean Mathematical Society
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    • v.40 no.4
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    • pp.663-669
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    • 2003
  • This paper investigates the tail asymptotic behavior of the severity of ruin (the deficit at ruin) in the renewal model. Under the assumption that the tail probability of the claimsize is dominatedly varying, a uniform asymptotic formula for the tail probability of the deficit at ruin is obtained.

Computing the Ruin Probability of Lévy Insurance Risk Processes in non-Cramér Models

  • Park, Hyun-Suk
    • Communications for Statistical Applications and Methods
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    • v.17 no.4
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    • pp.483-491
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    • 2010
  • This study provides the explicit computation of the ruin probability of a Le¢vy process on finite time horizon in Theorem 1 with the help of a fluctuation identity. This paper also gives the numerical results of the ruin probability in Variance Gamma(VG) and Normal Inverse Gaussian(NIG) models as illustrations. Besides, the paths of VG and NIG processes are simulated using the same parameter values as in Madan et al. (1998).

A M-TYPE RISK MODEL WITH MARKOV-MODULATED PREMIUM RATE

  • Yu, Wen-Guang
    • Journal of applied mathematics & informatics
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    • v.27 no.5_6
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    • pp.1033-1047
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    • 2009
  • In this paper, we consider a m-type risk model with Markov-modulated premium rate. A integral equation for the conditional ruin probability is obtained. A recursive inequality for the ruin probability with the stationary initial distribution and the upper bound for the ruin probability with no initial reserve are given. A system of Laplace transforms of non-ruin probabilities, given the initial environment state, is established from a system of integro-differential equations. In the two-state model, explicit formulas for non-ruin probabilities are obtained when the initial reserve is zero or when both claim size distributions belong to the $K_n$-family, n $\in$ $N^+$ One example is given with claim sizes that have exponential distributions.

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Surplus Process Perturbed by Diffusion and Subject to Two Types of Claim

  • Choi, Seung Kyoung;Won, Hojeong;Lee, Eui Yong
    • Communications for Statistical Applications and Methods
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    • v.22 no.1
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    • pp.95-103
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    • 2015
  • We introduce a surplus process which follows a diffusion process with positive drift and is subject to two types of claim. We assume that type I claim occurs more frequently, however, its size is stochastically smaller than type II claim. We obtain the ruin probability that the level of the surplus becomes negative, and then, decompose the ruin probability into three parts, two ruin probabilities caused by each type of claim and the probability that the level of the surplus becomes negative naturally due to the diffusion process. Finally, we illustrate a numerical example, when the sizes of both types of claim are exponentially distributed, to compare the impacts of two types of claim on the ruin probability of the surplus along with that of the diffusion process.

UNIFORM ASYMPTOTICS FOR THE FINITE-TIME RUIN PROBABILITY IN A GENERAL RISK MODEL WITH PAIRWISE QUASI-ASYMPTOTICALLY INDEPENDENT CLAIMS AND CONSTANT INTEREST FORCE

  • Gao, Qingwu;Yang, Yang
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.2
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    • pp.611-626
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    • 2013
  • In the paper we study the finite-time ruin probability in a general risk model with constant interest force, in which the claim sizes are pairwise quasi-asymptotically independent and arrive according to an arbitrary counting process, and the premium process is a general stochastic process. For the case that the claim-size distribution belongs to the consistent variation class, we obtain an asymptotic formula for the finite-time ruin probability, which holds uniformly for all time horizons varying in a relevant infinite interval. The obtained result also includes an asymptotic formula for the infinite-time ruin probability.

Computing Ruin Probability Using the GPH Distribution (GPH 분포를 이용한 파산확률의 계산)

  • Yoon, Bok Sik
    • Journal of the Korean Operations Research and Management Science Society
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    • v.40 no.3
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    • pp.39-48
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    • 2015
  • Even though ruin probability is a fundamental value to determine the insurance premium and policy, the complexity involved in computing its exact value forced us resort to an approximate method. In this paper, we first present an exact method to compute ruin probability under the assumption that the claim size has a GPH distribution, Then, for the arbitrary claim size distribution, we provide a method computing ruin probability quite accurately by approximating the distribution as a GPH. The validity of the proposed method demonstrated by a numerical example. The GPH approach seems to be valid for heavy-tailed claims as well as usual light-tailed claims.

An Improvement of the Approximation of the Ruin Probability in a Risk Process (보험 상품 파산 확률 근사 방법의 개선 연구)

  • Lee, Hye-Sun;Choi, Seung-Kyoung;Lee, Eui-Yong
    • The Korean Journal of Applied Statistics
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    • v.22 no.5
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    • pp.937-942
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    • 2009
  • In this paper, a continuous-time risk process in an insurance business is considered, where the premium rate is constant and the claim process forms a compound Poisson process. We say that a ruin occurs if the surplus of the risk process becomes negative. It is practically impossible to calculate analytically the ruin probability because the theoretical formula of the ruin probability contains the recursive convolutions and infinite sum. Hence, many authors have suggested approximation formulas of the ruin probability. We introduce a new approximation formula of the ruin probability which extends the well-known De Vylder's and exponential approximation formulas. We compare our approximation formula with the existing ones and show numerically that our approximation formula gives closer values to the true ruin probability in most cases.

ASYMPTOTIC RUIN PROBABILITIES IN A GENERALIZED JUMP-DIFFUSION RISK MODEL WITH CONSTANT FORCE OF INTEREST

  • Gao, Qingwu;Bao, Di
    • Journal of the Korean Mathematical Society
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    • v.51 no.4
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    • pp.735-749
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    • 2014
  • This paper studies the asymptotic behavior of the finite-time ruin probability in a jump-diffusion risk model with constant force of interest, upper tail asymptotically independent claims and a general counting arrival process. Particularly, if the claim inter-arrival times follow a certain dependence structure, the obtained result also covers the case of the infinite-time ruin probability.

RUIN PROBABILITIES IN THE RISK MODEL WITH TWO COMPOUND BINOMIAL PROCESSES

  • Zhang, Mao-Jun;Nan, Jiang-Xia;Wang, Sen
    • Journal of applied mathematics & informatics
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    • v.26 no.1_2
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    • pp.191-201
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    • 2008
  • In this paper, we consider an insurance risk model governed by a compound Binomial arrival claim process and by a compound Binomial arrival premium process. Some formulas for the probabilities of ruin and the distribution of ruin time are given, we also prove the integral equation of the ultimate ruin probability and obtain the Lundberg inequality by the discrete martingale approach.

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Ruin Probability in a Compound Poisson Risk Model with a Two-Step Premium Rule (이단계 보험요율의 복합 포아송 위험 모형의 파산 확률)

  • Song, Mi-Jung;Lee, Ji-Yeon
    • Communications for Statistical Applications and Methods
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    • v.18 no.4
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    • pp.433-443
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    • 2011
  • We consider a compound Poisson risk model in which the premiums may depend on the state of the surplus process. By using the overflow probability of the workload process in the corresponding M/G/1 queueing model, we obtain the probability that the ruin occurs before the surplus reaches a given large value in the risk model. We also examplify the ruin probability in case of exponential claims.