常利率下相依风险模型的破产问题

考虑常利率下理赔时间间隔与理额赔相依的风险模型.利用Laplace变换,首先得到了该模的生存概率和破产概率的Laplace变换满足的一阶齐次微分方程,其次得到了生存概率满足的指数积分方程.     

盈余过程服从跳扩模型下的破产概率

为了更真实地反映市场随机变化趋势,将经典的扩散模型推广到跳跃-扩散模型.用布朗运动和复合泊松过程共同驱动保险公司的盈余过程,并考虑盈余过程的系数受马尔可夫链干扰的情况.采用鞅方法和微积分方法研究保险公司的破产概率,得到破产概率所满足的偏微分方程.     

盈余过程服从跳扩模型下的破产概率

为了更真实地反映市场随机变化趋势,将经典的扩散模型推广到跳跃-扩散模型.用布朗运动和复合泊松过程共同驱动保险公司的盈余过程,并考虑盈余过程的系数受马尔可夫链干扰的情况.采用鞅方法和微积分方法研究保险公司的破产概率,得到破产概率所满足的偏微分方程.     

考虑投资收益的双险种二项风险模型的破产概率

在经典风险模型的基础上,考虑到投资收益的情况,讨论了保费收取次数和索赔过程均为二项分布的双险种风险模型,得到了模型的破产概率表达式及Lundberg不等式.     

逐段决定复合泊松风险模型的最优分红与注资策略

研究了逐段决定复合泊松风险模型的最优分红和注资问题,以股东的破产时刻折现分红减去惩罚折现注资的差的期望值最大化为目标,通过求解相应的HJB方程,得到了对应的值函数,进而得出最优分红和注资策略是Threshold策略的结论,使风险模型更加符合实际,更具现实意义.     

双复合二项风险模型的破产概率

在随机利率下,考虑资产组合的投资收益下单位时间内收到保单数和索赔次数都符合二项分布的风险模型,对模型的调节系数和破产概率等重要结论进行了研究,建立了更为客观实际的双险种风险经营模型,给出模型在初始准备金u=U(0)时的破产概率Ψ(u)在某些特殊情形下的表达式.     

一类四阶时滞微分方程的无条件稳定性

利用定性分析方法、代数方程根的性质及对数范数,研究了一类四阶时滞微分方程的无条件稳定性及实例的振动性,得到了该时滞微分方程无条件稳定性的充要条件,四次多项式函数在[-1,1]上无零点的充要条件.举出实例并用Matlab绘出了模型数值解的拟合图像.     

电力系统随机小扰动区间稳定性分析

通过建立含异步风力发电机组的电力系统随机不确定动态模型,基于随机微分方程、矩阵论等相关理论,给出系统依概率稳定定理,构造Lyapunov函数,并利用微分算子分析包含参数摄动的异步风力发电机组的随机小扰动区间稳定性.仿真结果验证了本文所提出的考虑参数摄动的电力系统依概率稳定定理的有效性.     

测测你的射点球理想角度

本论文是反馈性的,即读者输入客观上认为自己射门射得很歪的概率和最小角度,就能得到待测人射点球时的理想射门角度。我们先建立偏离角度和概率的关系的函数模型,得到函数方程,然后根据读者提供数据确定读者的函数的参数。最后,通过求函数积分的最大值(即射中概率)得到读者的射点球最佳角度。     

基于极值思想的高压油管压力控制

文章针对2019年"高教杯"全国大学生数学建模竞赛A题——高压油管的压力控制,运用了动态平衡原理、夹逼原则及临界条件下的极值思想,构建了流体力学模型、基于分段函数积分及连续微分方程的燃油流量计算模型、基于运筹学理论的目标规划模型等,并综合运用了MATLAB、EXCEL和LINGO等软件进行数据拟合和编程求解,得出单向阀开启时长的控制方案,使高压油管内压力在一定情况下尽可能稳定为某一常量。     

同步齿形带传动的优化设计

以带长、带宽、中心距作为目标函数,对齿形带结构参数的优化设计进行了探讨.例题中使用了内点惩罚函数法.文中的公式可用于齿形带的程序设计中.     

工业锅炉燃烧过程的稳态优化模型

建立了一个以能源成本最低为目标、采用神经网络模拟约束条件的工业锅炉燃烧过程稳态优化模型.介绍了该模型的罚函数法求解算法,并给出了一个应用实例.理论计算和实际使用表明,该模型有相当的精度,可以显著提高系统的能源利用率.     

基于罚函数法的模切机前靠规凸轮设计

针对控制型凸轮的工作特点,提出了以尺寸极小化作为目标函数的优化方法及优化模型,采用罚函数算法。通过编程运算,得到了较理想的设计结果,并在模切机中得到了成功应用。     

Relationships of first lactation milk and type traits to cow survival and a sire index for discounted total milk

The probability of cow survival during each of six consecutive 13-mo periods after first calving was regressed on lactation milk yield and 15 type traits, each recorded during the first lactation. Adjusted coefficients of determination were small (.028 to .081). The ratio of variance in predicted cow survival probabilities due to milk only with that due to the 15 type traits was 12.6:1, 4.7:1, 2.5:1, .5:1, 0:1, and .02:1 for respective herdlife periods. Maximum effect of type traits on herdlife ranged from 11 to 109 d. Prediction equations for cow survival were incorporated into a sire index for discounted total milk yield of progeny. Type traits affected the sire index by their influence on the six predicted survival rates. Milk yield affected the discounted total milk index directly as well as through the survival rates. Simulated variation from milk estimated transmitting abilities for sires accounted for 99.9% of the total variation in the discounted total milk index. Since the effect of the type traits on cow survival rates was greatest during the later herdlife periods, too few animals would have survived to these later periods to reveal any significant effect from type on the discounted total milk index.     

Uncertainty of air pollution cost estimates: to what extent does it matter?

How large is the social cost penalty if one makes the wrong choice because of uncertainties in the estimates of the costs and benefits of environmental policy measures? For discrete choices there is no general rule other than the recommendation to always carefully compare costs and benefits when introducing policies for environmental protection. For continuous choices (e.g., the ceiling for the total emissions of a pollutant by an entire sector or region), it is instructive to look at the cost penalty as a function of the error in the incremental damage cost estimate. Using abatement cost curves for NOx, SO2, dioxins, and CO2, this paper evaluates the cost penalty for errors in the following: national emission ceilings for NOx and SO2 in each of 12 countries of Europe, an emission ceiling for dioxins in the UK, and limits for the emission of CO2 in Europe. The cost penalty turns out to be remarkably insensitive to errors. An error by a factor of 3 due to uncertainties in the damage estimates for NOx and SO2 increases the total social cost by at most 20% and in most cases much less. For dioxins, the total social cost is increased by at most 10%. For CO2, several different possible cost curves are examined: for some the sensitivity to uncertainties is greater than for the other pollutants, but even here the penalty is less than 30% and in most cases much less if the true damage costs are twice as high as the ones estimated. The paper also quantifies the benefit of improving the accuracy of damage cost estimates by further research.     

间歇蒸煮过程的分层多目标优化

对制浆生产间歇蒸煮过程进行了详细分析，建立了包括环境污染为目标函数的多目标分层规划数学模型，将传统分层多目标优化的方法和遗传算法相结合，提出了一种新的目标优化方法，遗传算法中综合并列选择和小生境方法，采用了池点编码和算术交叉操作，应用罚数法将有约束优化问题转化成无约束优化问题，应用实际间歇蒸煮过程数据的优化仿真结果表明，该方法可以在保证纸浆质量的前提下，减少排放废液中碱的含量，降低生产成本，达到清洁生产的目的。     

Short communication: Bulk milk somatic cell penalties in herds enrolled in Dairy Herd Improvement programs

The objective of this study was to determine the effect of somatic cell count (SCC) monitoring at the cow level through Dairy Herd Improvement (DHI) programs on the risk of bulk tank SCC (BTSCC) penalties. For the year 2009, BTSCC for all producers in Ontario were examined, for a total of 2,898 DHI herds, 1,186 non-DHI herds, and 48,250 BTSCC records. Two penalty levels were examined, where BTSCC exceeded 499,000 (P500) and 399,000 (P400) cells/mL. Data were modeled first to determine the odds of a BTSCC exceeding a set penalty threshold and second to determine the odds of incurring a penalty under the Ontario Milk Act. All data were modeled as a generalized mixed model with a binary link function. Random effects included herd, fixed effects included season of BTSCC (summer, May to September, and winter, October to April), total milk shipped per month (L), fat paid per month (kg), protein paid per month (kg), and participation or not in the DHI program. The likelihood of a BTSCC exceeding a penalty threshold in a non-DHI herd compared with a DHI herd was significantly greater than 1 at both penalty levels, where the odds ratios were estimated to be 1.42 [95% confidence interval (CI): 1.19 to 1.69] and 1.38 (95% CI: 1.25 to 1.54) for P500 and P400, respectively. The likelihood of incurring a BTSCC penalty (where 3 out of 4 consecutive BTSCC exceeded penalty thresholds) was not significantly different at P500; however, it was significantly different for P400, where the odds ratio was estimated to be 1.42 (95% CI: 1.12 to 1.81).     

带跳的具有卖空限制的证券投资组合选择问题

研究了股票价格服从跳跃扩散过程的具有限制卖空约束的均值-方差投资组合选择问题.首先建立一个最优随机LQ问题,由于此问题具有限制卖空约束,因此传统的Riccati方程理论就不再适用,另外与之相关的HJB方程也不存在光滑解.通过2个Riccati方程构建一个连续函数,并证明这个函数就是HJB方程的粘性解.最后通过解Riccati方程得到原始均值-方差问题的有效边界和最优投资策略.