Some new classes of stochastic order relations among arithmetic random variables, with applications in actuarial sciences

Recently, Fishbum and Lavalle (1995) and Lefèvre and Utev (1996) have considered some stochastic order relations specific for arithmetic random variables. The present work is concerned with these orderings, together with two other classes of stochastic order relations closely related. First, attention is paid to characterizations and various properties of all these orderings. Then, sufficient conditions of crossing-type for the two new classes of orderings are derived and extrema among discrete random variables are deduced. This is applied in actuarial sciences to obtain new bounds for the classical single life premiums as well as for the probability of ruin in the compound binomial risk model.     

Locally Adaptive Wavelet Empirical Bayes Estimation of a Location Parameter

The traditional empirical Bayes (EB) model is considered with the parameter being a location parameter, in the situation when the Bayes estimator has a finite degree of smoothness and, possibly, jump discontinuities at several points. A nonlinear wavelet EB estimator based on wavelets with bounded supports is constructed, and it is shown that a finite number of jump discontinuities in the Bayes estimator do not affect the rate of convergence of the prior risk of the EB estimator to zero. It is also demonstrated that the estimator adjusts to the degree of smoothness of the Bayes estimator, locally, so that outside the neighborhoods of the points of discontinuities, the posterior risk has a high rate of convergence to zero. Hence, the technique suggested in the paper provides estimators which are significantly superior in several respects to those constructed earlier.     

Large Sample Properties of Mixture Models with Covariates for Competing Risks

We study the large-sample properties of a class of parametric mixture models with covariates for competing risks. The models allow general distributions for the survival times and incorporate the idea of long-term survivors. Asymptotic results are obtained under a commonly assumed independent censoring mechanism and some modest regularity conditions on the survival distributions. The existence, consistency, and asymptotic normality of maximum likelihood estimators for the parameters of the model are rigorously derived under general sufficient conditions. Specific conditions for particular models can be derived from the general conditions for ready check. In addition, a likelihood-ratio statistic is proposed to test various hypotheses of practical interest, and its asymptotic distribution is provided.     

Likelihood Inference under Generalized Hybrid Censoring Scheme with Comp eting Risks

Statistical inference is developed for the analysis of generalized type-II hybrid censoring data under exponential competing risks model. In order to solve the problem that approximate methods make unsatisfactory performances in the case of small sample size, we establish the exact conditional distributions of estimators for parameters by conditional moment generating function(CMGF). Furthermore, confidence intervals(CIs) are constructed by exact distributions, approximate distributions as well as bootstrap method respectively, and their performances are evaluated by Monte Carlo simulations. And finally, a real data set is analyzed to illustrate all the methods developed here.     

Risk externalities and too big to fail

This paper establishes the case for a fallacy of economies of scale in large aggregate institutions and the effects of scale risks. The problem of rogue trading and excessive risk taking is taken as a case example. Assuming (conservatively) that a firm exposure and losses are limited to its capital while external losses are unbounded, we establish a condition for a firm not to be allowed to be too big to fail. In such a case, the expected external losses second derivative with respect to the firm capital at risk is positive. Examples and analytical results are obtained based on simplifying assumptions and focusing exclusively on the risk externalities that firms too big to fail can have.     

An overview of emerging pollutants in air: Method of analysis and potential public health concern from human environmental exposure

Air pollutants are perhaps the largest cause of diseases and death in the world today. Increasing urbanization and industrialization have caused an increase in number of diverse forms and types of new pollutants, which are difficult to detect and characterize due to their stench behaviour and complex sources of production. Such pollutants have been called emerging pollutants (EPs) and their list is ever increasing. Therefore, the understanding of the method of analysis and health implication of (EPs) in air is critical to providing a more robust understanding of exposure routes, regulations and mitigation. EPs in air discussed in this study are not in any way exhaustive but limited to emerging VOCs (including acrylonitrile, 1−3-butadiene, chloroform, dichloromethane, ethylene oxides, formaldehyde, toluene, trichloroethylene, 1,4-Dioxane) and metals (arsenic, manganese, and vanadium), ultrafine particles, micro- and nano- plastics, engineered nanoparticles, diesel/black carbon and bioaerosols. Occurrence, detection and health implications of these EPs in air are still unfolding due to limited monitoring studies, lack of standard methodology and regulations. To address this knowledge gap, authors conducted an in-depth review of available information. Their spatial distribution, analytical methods and health implications are discussed including the novel coronavirus (COVID-19) as a potential EP in air. The study concluded with highlights of gaps in knowledge and suggestions to key areas for future research. This information is of general interest to environmental scientists and of specific interest to both health and sanitation workers and policymakers at private, government and international organizations.     

电感耦合等离子体原子发射光谱(ICP-AES)法测定胡蜂酒中无机元素

采用电感耦合等离子体原子发射光谱法测定胡蜂酒中20种无机元素,建立无机元素对照指纹图谱,对重金属元素进行风险评估。结果表明,胡蜂酒中无机元素种类丰富,其中P、K、Na元素占测定总元素的96.14%。有害元素Pb、Cd、As、Hg、Cu含量符合国家药典标准要求,Cu的靶标危险系数(THQ)为1.00×10^-2,THQ<1说明摄入的重金属对人体健康造成的影响不明显。不同产区胡蜂酒金属元素含量存在差异,根据金属元素图谱得出元素含量按原子序数顺序出现相似的分布态势。结果表明,胡蜂酒中含有丰富的金属元素,很多为营养微量元素,有害元素(Pb、Cd、As、Hg、Cu)含量符合药典要求,从金属元素方面单一来看,饮用胡蜂酒没有明显的健康风险。胡蜂酒无机元素指纹图谱可为胡蜂酒的鉴别提供一定的的参考依据。     

开放式基金流动性指标研究

本文主要介绍了开放式投资基金的流动性概念和指标体系设计，并运用指标进行实证检验，分析基金的流动性及其实际意义。     

The fundamental theorem of mutual insurance

The essence of mutual insurance is the notion that re-distributing risk in a pool of risks is more beneficial than taking the risk alone. Interpreting ‘more beneficial’ as an increase in utility and considering sequences of exchangeable risks, we are able to formalize this notion from the policyholder’s perspective and demonstrate its validity for various alternative preference functionals (e.g., expected utility, Choquet expected utility, and distortion risk measures). To obtain this result, we exploit that for a sequence of exchangeable risks the corresponding sequence of arithmetical averages is a reversed martingale.We conclude that pooling risks is fundamental for understanding the mechanisms of insurance because it favourably affects the utility of policyholders, and we refer to this phenomenon as the ‘utility-improving effect of risk pooling’. Moreover, we demonstrate that the utility of the policyholder is (strictly) increasing with the size of the risk pool.     

Optimal proportional reinsurance with common shock dependence

In this paper, we consider the optimal proportional reinsurance strategy in a risk model with multiple dependent classes of insurance business, which extends the work of Liang and Yuen (2014) to the case with the reinsurance premium calculated under the expected value principle and to the model with two or more classes of dependent risks. Under the criterion of maximizing the expected exponential utility, closed-form expressions for the optimal strategies and value function are derived not only for the compound Poisson risk model but also for the diffusion approximation risk model. In particular, we find that the optimal reinsurance strategies under the expected value premium principle are very different from those under the variance premium principle in the diffusion risk model. The former depends not only on the safety loading, time and interest rate, but also on the claim size distributions and the counting processes, while the latter depends only on the safety loading, time and interest rate. Finally, numerical examples are presented to show the impact of model parameters on the optimal strategies.