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Equilibrium Reinsurance Strategy and Mean Residual Life Function
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作者 Dan-ping LI Lv CHEN +1 位作者 Lin-yi QIAN Wei WANG 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2024年第3期758-777,共20页
In this paper,we analyze the relationship between the equilibrium reinsurance strategy and the tail of the distribution of the risk.Since Mean Residual Life(MRL)has a close relationship with the tail of the distributi... In this paper,we analyze the relationship between the equilibrium reinsurance strategy and the tail of the distribution of the risk.Since Mean Residual Life(MRL)has a close relationship with the tail of the distribution,we consider two classes of risk distributions,Decreasing Mean Residual Life(DMRL)and Increasing Mean Residual Life(IMRL)distributions,which can be used to classify light-tailed and heavy-tailed distributions,respectively.We assume that the underlying risk process is modelled by the classical CramérLundberg model process.Under the mean-variance criterion,by solving the extended Hamilton-Jacobi-Bellman equation,we derive the equilibrium reinsurance strategy for the insurer and the reinsurer under DMRL and IMRL,respectively.Furthermore,we analyze how to choose the reinsurance premium to make the insurer and the reinsurer agree with the same reinsurance strategy.We find that under the case of DMRL,if the distribution and the risk aversions satisfy certain conditions,the insurer and the reinsurer can adopt a reinsurance premium to agree on a reinsurance strategy,and under the case of IMRL,the insurer and the reinsurer can only agree with each other that the insurer do not purchase the reinsurance. 展开更多
关键词 mean residual life excess-of-loss reinsurance INSURER reinsurer stochastic control
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The Proportional Mean Residual Life Regression Model with Cure Fraction and Auxiliary Covariate
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作者 Shao-jia JIN Yan-yan LIU +1 位作者 Guang-cai MAO Ming-yu SHAN 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2022年第2期312-323,共12页
As biological studies become more expensive to conduct,it is a frequently encountered question that how to take advantage of the available auxiliary covariate information when the exposure variable is not measured.In ... As biological studies become more expensive to conduct,it is a frequently encountered question that how to take advantage of the available auxiliary covariate information when the exposure variable is not measured.In this paper,we propose an induced cure rate mean residual life time regression model to accommodate the survival data with cure fraction and auxiliary covariate,in which the exposure variable is only assessed in a validation set,but a corresponding continuous auxiliary covariate is ascertained for all subjects in the study cohort.Simulation studies elucidate the practical performance of the proposed method under finite samples.As an illustration,we apply the proposed method to a heart disease data from the Study of Left Ventricular Dysfunction. 展开更多
关键词 auxiliary covariate Kernel smoothing logistic regression mean residual life mixture cure model
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Likelihood Ratio Inference for Mean Residual Life of Length-biased Random Variable
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作者 Wei LIANG Jun-shan SHEN Shu-yuan HE 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2016年第2期269-282,共14页
In lifetime data analysis, naturally recorded observations are length-biased data if the probability to select an item is proportional to its length. Based on i.i.d, observations of the true distribution, empirical li... In lifetime data analysis, naturally recorded observations are length-biased data if the probability to select an item is proportional to its length. Based on i.i.d, observations of the true distribution, empirical likelihood (EL) procedure is proposed for the inference on mean residual life (MRL) of naturally recorded item. The limit distribution of the EL based log-likelihood ratio is proved to be the chi-square distribution. Under right censorship, since the EL based log-likelihood ratio leads to a scaled chi-square distribution and estimating the scale parameter leads to lower coverage of confidence interval, we propose an algorithm to calculate the likelihood ratio (LR) directly. The corresponding log-likelihood ratio converges to the standard chi-square distribution and the corresponding confidence interval has a better coverage. Simulation studies are used to support the theoretical results. 展开更多
关键词 likelihood ratio length bias mean residual life right censoring
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Health evaluation method for degrading systems subject to dependent competing risks 被引量:3
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作者 ZHAO Shuai MAKIS Viliam +1 位作者 CHEN Shaowei LI Yong 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2018年第2期436-444,共9页
This paper proposes a health evaluation method for degrading systems subject to competing risks of dependent soft and hard failures. To characterize the time-varying degradation rate, the degradation process is determ... This paper proposes a health evaluation method for degrading systems subject to competing risks of dependent soft and hard failures. To characterize the time-varying degradation rate, the degradation process is determined by a non-stationary Gamma process and the soft failure is encountered when it exceeds a predefined critical level. For the hard failure, a Cox’s proportional hazard model is applied to describe the hazard rate of the time to system failure. The dependent relationship is modeled by incorporating the degradation process as a time-varying covariate into the Cox’s proportional hazard model. To facilitate the health characteristics evaluation, a discretization technique is applied both to the degradation process and the monitoring time.All health characteristics can be obtained in the explicit form using the transition probability matrix, which is computationally attractive for practical applications. Finally, a numerical analysis is carried out to show the effectiveness and the performance of the proposed health evaluation method. 展开更多
关键词 competing risk conditional mean residual life health evaluation non-stationary Gamma process proportional hazards model
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Applications of survival functions to continuous semi-Markov processes for measuring reliability of power transformers 被引量:2
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作者 Yifei WANG Mohammad SHAHIDEHPOUR Chuangxin GUO 《Journal of Modern Power Systems and Clean Energy》 SCIE EI 2017年第6期959-969,共11页
The reliability of power transformers is subject to service age and health condition.This paper proposes a practical model for the evaluation of two reliability indices:survival function(SF)and mean residual life(MRL)... The reliability of power transformers is subject to service age and health condition.This paper proposes a practical model for the evaluation of two reliability indices:survival function(SF)and mean residual life(MRL).In the proposed model,the periodical modeling of power transformers are considered for collecting the information on health conditions.The corresponding health condition is assumed to follow a continuous semi-Markov process for representing a state transition.The proportional hazard model(PHM)is introduced to incorporate service age and health condition into hazard rate.In addition,the proposed model derives the analytical formulas for and offers the analytical evaluation of SF and MRL.SF and MRL are calculated for new components and old components,respectively.In both cases,the proposed model offers rational results which are compared with those obtained from comparative models.The results obtained by the contrast of the proposed analytical method and the Monte Carlo method.The impact of differentmodel parameters and the coefficient of variation(CV)on reliability indices are discussed in the case studies. 展开更多
关键词 Power system reliability TRANSFORMERS Proportional hazard model Survival function mean residual life Semi-Markov process
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