含交易费用的证券组合投资模型的满意解

在证券组合投资过程中,忽略交易费用会导致非有效的证券组合投资,本文提出了一个考虑交易费用的证券组合投资的区间数线性规划模型,通过引入区间数线性规划问题中的目标函数优化水平参数λ和约束条件满足水平参数η将目标函数和约束条件均为区间数的区间数线性规划模型转化为确定型的一般线性规划模型,进而求得相应于优化水平λ和满足水平η的满意解.     

多因素指派模型全局优化问题研究

基于多因素资源优化分配问题的不确定性,建立基于区间数型下的不确定多因素指派模型,给出模型建立的理论依据与全局优化算法,拓展区间数型多因素指派模型,解决了不确定条件下多因素资源优化分配问题.考虑多因素影响,基于任务完成效率,以5类任务多因素分配问题为例,获得了指派模型全局优化的解.为不确定条件下资源优化分配问题的研究拓宽了决策途径.     

多目标运输问题的区间模型及其算法

主要给出一类目标函数的系数、供应量和需求量均为区间数的多目标运输问题模型,根据参数的实际意义和区间数的序关系,针对所建立模型,利用区间规划的方法,将其转化为确定型的多目标运输问题,最后用模糊规划技术处理等价的多目标运输问题.数值例子表明算法的有效性和可行性.     

基于模糊——随机规划的WEEE回收物流网络优化研究

针对废旧电子电气设备(WEEE)绿色回收问题,根据实际需求刻画其回收物流网络结构;在模型构建中.考虑参数为随机和模糊共存的情况,提出应用随机机会约束规划和模糊机会约束规划相结合的方法来建模;设模型参数是相互独立的,合理利用转换定理将不确定规划转变为常规数学规划,并借助LINGO软件求解最优方案.     

三参数区间灰数的多属性灰关联决策方法

针对决策信息不确定的多属性决策问题,利用三参数区间灰数的概率分布特征及经典灰关联决策的优势,提出了基于三参数区间灰数的灰关联决策方法.首先定义了三参数区间灰数决策向量与理想最优方案和临界方案决策向量的区间关联系数,其次得到所有方案决策向量的区间综合关联度,由区间综合关联度最大化和灰熵最大化确定属性的权重,进而对方案进行择优排序,最后用算例说明决策模型的合理性和实用性.     

考虑不确定因素影响的沉淀池优化设计

沉淀池是污水处理流程中一个必不可少的重要环节,设计中存在着大量的不确定因素.本文在沉淀池设计中引入了不确定性模糊非线性规划模型.该模型利用处理效率与沉淀池尺寸之间的非线性关系,求解过程引入区间数和模糊算子,尝试在沉淀池设计中考虑不确定性因素,并取得满意的结果.     

基于区间数的证券组合投资模型研究

提出了证券组合投资的区间数线性规划模型.通过引入区间数线性规划问题中的目标函数优化水平α和约束水平β将目标函数和约束条件均为区间数的线性规划问题转化为确定型的线性规划问题.投资者可以根据自己的风险喜好程度和客观情况,对这两个参数做出不同的估计,从而得到相应情况下的有效投资方案,使证券组合投资决策更具柔性.最后通过实例分析说明了该模型的可行性.     

实时定期人寿保险的破产模型及破产概率的计算

研究定期人寿保险中破产风险问题。建立了该类问题的数学模型,并分析其结构特征,推导破产概率的计算公式,并设计其计算方法。同以往模型相比,新模型的建立考虑了初始准备金的利息积累和任何时刻的新投保人的加入,采用了新的分组方式。这种新模型更加真实地刻画了实际过程,保证了传统模型中常用的某些假设得到了满足。     

基于矩阵型时滞灰色多变量模型的区间数序列预测

许多数据表示为区间数时更有利于管理和决策.为有效预测区间数序列,考虑系统中普遍存在的时滞效应,基于传统灰色模型同时引入系统特征和相关因素的滞后项,然后进一步把模型的适用范围从精确数序列拓广到区间数序列,提出了矩阵型时滞灰色多变量模型.在此基础上,提出了一种确定区间数序列最优滞后阶的方法.最后对我国财政收入和社会消费品零售总额进行预测,结果表明新模型是有效的,在拟合和预测方面均优于其他五个灰色竞争模型,具有一定的应用价值.     

基于区间效率的贷款定价研究

以存款利息支出率、费用支出率、预期违约损失率、目标利润率等4个定价指标作为输入,以贷款利率作为输出,采用支持向量机回归算法建立基于区间效率的贷款定价模型.创新与特色一是通过区间数形式来反映预期违约损失率、目标利润率、费用支出率等,改变了现有研究将目标利润、贷款费用、违约损失等变量看作确定性数值来定价的现状.使贷款利率更具有竞争性.二是通过比较不同核函数、核参数下的训练样本的贷款效率区间与合理的贷款效率区间的匹配程度,确定贷款定价模型最优的核函数和核参数,进而建立了贷款定价模型.间接解决了在考虑贷款价格能否被银行、客户接受情况下贷款利率确定的问题.     

考虑银行破产外部效应的存款保险定价模型

运用存款保险的期望损失定价方法和Shapley值法,建立了考虑银行违约/破产外部效应的存款保险定价模型。模型中度量的破产成本不仅考虑了银行破产清算过程中其自身资产价值的损失,还考虑了银行违约/破产的负外部效应——可能增加其他银行的破产损失,据此确定的存款保险保费反映了各银行对系统总破产成本的边际贡献。为验证模型效果,构造了三种情景进行模拟分析,结果表明:存款保险保费与银行系统对破产银行资产的收购能力负相关,且负相关程度随经济形势的恶化而加剧;保费与整个银行系统参保银行数目之间也呈负相关关系。     

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??We develop a deposit insurance pricing model that explicitly considers regulatory capital and bankruptcy costs. Based on the pricing deposit insurance model, we calculate the deposit insurance premiums of China's 16 listed banks with time span of 2011 to 2017 in this paper. The results demonstrate that the deposit insurance premiums of state-owned banks is lower than joint-stock commercial banks and city commercial banks, however, the deposit insurance premiums of joint-stock commercial banks is higher than city commercial banks. Numerical simulation shows that, ceteris paribus, the value of deposit insurance decreases with regulatory capital ratios and the insured deposits ratios, but it increases with interest rate and bankruptcy costs.     

Ornstein-Uhlenback type Omega model

We consider the Omega model with underlying Ornstein-Uhlenbeck type surplus process for an insurance company and obtain some useful results. Explicit expressions for the expected discounted penalty function at bankruptcy with a constant bankruptcy rate and linear bankruptcy rate are derived. Based on random observations of the surplus process, we examine the differentiability for the expected discounted penalty function at bankruptcy especially at zero. Finally, we give the Laplace transforms for occupation times as an important example of Li and Zhou [Adv. Appl. Probab., 2013, 45(4): 1049–1067].     

The Pricing of Deposit Insurance Considering Regulatory Capital and Bankruptcy Cost

We develop a deposit insurance pricing model that explicitly considers regulatory capital and bankruptcy costs. Based on the pricing deposit insurance model, we calculate the deposit insurance premiums of China's 16 listed banks with time span of 2011 to 2017 in this paper. The results demonstrate that the deposit insurance premiums of state-owned banks is lower than joint-stock commercial banks and city commercial banks, however, the deposit insurance premiums of joint-stock commercial banks is higher than city commercial banks. Numerical simulation shows that, ceteris paribus, the value of deposit insurance decreases with regulatory capital ratios and the insured deposits ratios, but it increases with interest rate and bankruptcy costs.     

Modeling the number of insureds’ cars using queuing theory

In this paper, we propose to model the number of insured cars per household. We use queuing theory to construct a new model that needs 4 different parameters: one that describes the rate of addition of new cars on the insurance contract, a second one that models the rate of removal of insured vehicles, a third parameter that models the cancellation rate of the insurance policy, and finally a parameter that describes the rate of renewal. Statistical inference techniques allow us to estimate each parameter of the model, even in the case where there is censorship of data. We also propose to generalize this new queuing process by adding some explanatory variables into each parameter of the model. This allows us to determine which policyholder’s profiles are more likely to add or remove vehicles from their insurance policy, to cancel their contract or to renew annually. The estimated parameters help us to analyze the insurance portfolio in detail because the queuing theory model allows us to compute various kinds of useful statistics for insurers, such as the expected number of cars insured or the customer lifetime value that calculates the discounted future profits of an insured. Using car insurance data, a numerical illustration based on a portfolio from a Canadian insurance company is included to support this discussion.     

Mean-risk portfolio management with bankruptcy prohibition

In accordance with Solvency II, the commonly tightened government regulation on insurance cooperations, they have been obligated to take conservative investment strategies such as those ruling out the possibility of bankruptcy. With this in mind, in this article, we aim to continue our work (Wong et al., 2017a,b) . First, we study the solvability of mean-risk portfolio optimization problem with bankruptcy prohibition, in the complete market in which the investor aims to maximize the expected payoff and to minimize the deviation risk simultaneously, which is of great use in the insurance paradigm. Secondly, we also provide the original weak convergence result of the optimal terminal wealth of a sequence of approximate markets to that of the limiting market through their corresponding pricing kernels. As a result, we establish an effective numerical algorithm calibrating the optimal terminal wealth under Black–Scholes models by that of binomial tree models. The results of our numerical simulations indicate that the downside risk of the optimal payoff can be effectively reduced by imposing the bankruptcy prohibition.     

Optimal dividend and dynamic reinsurance strategies with capital injections and proportional costs

We consider an optimization problem of an insurance company in the diffusion setting, which controls the dividends payout as well as the capital injections. To maximize the cumulative expected discounted dividends minus the penalized discounted capital injections until the ruin time, there is a possibility of (cheap or non-cheap) proportional reinsurance. We solve the control problems by constructing two categories of suboptimal models, one without capital injections and one with no bankruptcy by capital injection. Then we derive the explicit solutions for the value function and totally characterize the optimal strategies. Particularly, for cheap reinsurance, they are the same as those in the model of no bankruptcy.     

Estimating the distortion parameter of the proportional-hazard premium for heavy-tailed losses

The distortion parameter reflects the amount of loading in insurance premiums. A specific value of a given premium determines a value of the distortion parameter, which depends on the underlying loss distribution. Estimating the parameter, therefore, becomes a statistical inferential problem, which has been initiated by Jones and Zitikis [Jones, B.L., Zitikis, R., 2007. Risk measures, distortion parameters, and their empirical estimation. Insurance: Mathematics and Economics, 41, 279–297] in the case of the distortion premium and tackled within the framework of the central limit theorem. Heavy-tailed losses do not fall into this framework as they rely on the extreme-value theory. In this paper, we concentrate on a special but important distortion premium, called the proportional-hazard premium, and propose an estimator for its distortion parameter in the case of heavy-tailed losses. We derive an asymptotic distribution of the estimator, construct a practically implementable confidence interval for the distortion parameter, and illustrate the performance of the interval in a simulation study.