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This article presents a Poisson common factor model with an overdispersion factor to predict some multiple populations' mortality rates. We use Bayesian data analysis and an extension of the Hamiltonian Monte Carlo sampler to compute the estimation of the model parameters and mortality rates prediction. We apply the proposed model to the real mortality data of some European countries. Using some model selection measures, we compare the proposed model with a log-linear model and those introduced in Antonio, Bardoutsos, and Ouburg (2015, Bayesian Poisson log-bilinear models for mortality projections with multiple populations. European Actuarial Journal 5 (2): 245–281) and Wong, Forster, and Smith (2018, Bayesian mortality forecasting with overdispersion. Insurance: Mathematics and Economics 83: 206–221). [ABSTRACT FROM AUTHOR]

Prediction of loss reserves corresponding to dependent lines of business is one of the most important problems in the actuarial sciences. In this paper, we propose a class of copula based multivariate distributions to model the losses with the heavy tailed distribution in the run-off triangles to predict unpaid losses. We set up ANOVA, ANCOVA, and state space models with four choices of copulas, Clayton, Frank, Gumbel, and Gaussian to provide a new procedure for analyzing run-off triangle tables. We use the Hamiltonian Monte Carlo sampler to perform a Bayesian analysis to estimate the parameters. We apply the proposed models to the data set consists of two lines of business of paid losses data from the Schedule P of the National Association of Insurance Commissioners (NAIC) database. Using some well known criteria, we compare the prediction accuracy of the mean models. As a result, the ANCOVA model with the Clayton copula dominates the other models. [ABSTRACT FROM AUTHOR]

In the usual shock models, the shocks arrive from a single source. Bozbulut and Eryilmaz [(2020). Generalized extreme shock models and their applications. Communications in Statistics – Simulation and Computation 49 (1): 110–120] introduced two types of extreme shock models when the shocks arrive from one of $m\geq 1$ possible sources. In Model 1, the shocks arrive from different sources over time. In Model 2, initially, the shocks randomly come from one of $m$ sources, and shocks continue to arrive from the same source. In this paper, we prove that the lifetime of Model 1 is less than Model 2 in the usual stochastic ordering. We further show that if the inter-arrival times of shocks have increasing failure rate distributions, then the usual stochastic ordering can be generalized to the hazard rate ordering. We study the stochastic behavior of the lifetime of Model 2 with respect to the severity of shocks using the notion of majorization. We apply the new stochastic ordering results to show that the age replacement policy under Model 1 is more costly than Model 2. [ABSTRACT FROM AUTHOR]

We consider n risks X 1 , X 2 , ... , X n insured by a layer coverage with deductibles and limits given by (d 1 , l 1) , ... , (d n , l n) , respectively. We investigate the optimal allocation of insurance layers from the viewpoint of the insurer. We derive lower and upper bounds for the survival function of the smallest and largest claim amounts using the first stochastic dominance order. We find that assigning a small deductible and a large limit to large risks increases (decreases) stop-loss premiums of the largest (smallest) claim amounts. [ABSTRACT FROM AUTHOR]

The transformer network is a deep learning architecture that uses selfattention mechanisms to capture the long-term dependencies of a sequential data. The Poisson-Lee-Carter model, introduced to predict mortality rate, includes the factors of age and the calendar year, which is a time-dependent component. In this paper, we use the transformer to predict the time-dependent component in the Poisson-Lee-Carter model. We use the real mortality data set of some countries to compare the mortality rate prediction performance of the transformer with that of the long short-term memory (LSTM) neural network, the classic ARIMA time series model and simple exponential smoothing method. The results show that the transformer dominates or is comparable to the LSTM, ARIMA and simple exponential smoothing method. [ABSTRACT FROM AUTHOR]

Mean time to failure in age replacement evaluates the performance and effectiveness of the age replacement policy. In this paper, we propose a test for exponentiality against a trend change in mean time to failure in age replacement. We derive the asymptotic distribution of the test statistics under the null hypothesis to approximate the critical values. We conduct a simulation study to investigate the performance of the proposed test. To illustrate the application, we apply our test on a real data set. [ABSTRACT FROM AUTHOR]

Suppose that a policyholder faces n risks X1;: ::;Xn which are insured under the policy limit with the total limit of l. Usually, the policyholder is asked to protect each Xi with an arbitrary limit of li such that Pni =1 li = l. If the risks are independent and identically distributed with log-concave cumulative distribution function, using the notions of majorization and stochastic orderings, we prove that the equal limits provide the maximum of the expected utility of the wealth of policyholder. If the risks with log-concave distribution functions are independent and ordered in the sense of the reversed hazard rate order, we show that the equal limits is the most favourable allocation among the worst allocations. We also prove that if the joint probability density function is arrangement increasing, then the best arranged allocation maximizes the utility expectation of policyholder's wealth. We apply the main results to the case when the risks are distributed according to a log-normal distribution. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of optimal allocation of insurance layers for a portfolio of i.i.d exponential risks. Using the first stochastic dominance criterion, we obtain an optimal allocation for the total retain risks faced by a policyholder. This result partially generalizes the known result in the literature for deductible as well as policy limit coverages. [ABSTRACT FROM AUTHOR]

SupposeFandGare two life distribution functions. It is said thatFis more IFRA (increasing failure rate average) thanG(written byF⩽*G) ifG− 1F(x) is star-shaped on (0, ∞). In this paper, the problem of testingH0:F=*GagainstH1:F⩽*GandF≠*Gis considered in both cases whenGis known and whenGis unknown. We propose a new test based on U-statistics and obtain the asymptotic distribution of the test statistics. The new test is compared with some well-known tests in the literature. In addition, we apply our test to a real data set in the context of reliability. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the component importance in k -out-of- n system with components having random weights. The system works if at least k components work and the total weight of all working components is above the required level c . A new measure of component importance, called weighted importance , for such a system is introduced and its relation with Birnbaum reliability measure of importance is studied. It is shown that the larger weight stochastically implies the larger weighted measure of importance. It is also shown that if two components are identically distributed then the larger weight stochastically implies the larger Birnbaum reliability measure of importance. Finally, it is proved that if the weight of a component is stochastically increased, then the weighted and Birnbaum reliability measures of importance are increased accordingly. [ABSTRACT FROM AUTHOR]