跳跃自激发与非对称交叉回馈机制下的期权定价研究

跳跃集聚和波动率非对称回馈是股票价格运动过程中不可忽视的重要特征.基于动态跳-扩散半鞅随机过程,本文提出了具有时变跳跃到达率和波动率的双因子交叉回馈机制的期权定价模型,推导了跳-扩散交叉回馈模型的一般化风险中性变换关系;同时借助序贯贝叶斯方法对模型和跳跃风险溢价进行校准,并对道琼斯工业平均指数(DJX)、标普500指数(SPX)、苹果(APL)、IBM、JP摩根(JPM)股票进行实证研究,研究发现,它们的跳跃达到率和波动率都呈现集聚性和非对称回馈效应,且跳跃到达率具有更强的持续性和更大的杠杆系数;跳跃风险溢价在定价中占主要地位.期权定价的实证研究还表明,双因子交叉回馈模型具有最小的期权定价误差,定价能力明显优于单向回馈的跳-扩散模型.     

熔池自激振荡的力学模型

本文提出熔池内钢水波动过程中的粘性损耗、回流运动与气泡上浮的能量可互为补偿,形成接近于无损的“自激振荡”式的波动。经过近似处理,推导出自激振荡的力学模型。在水模实验中可以看到,气泡上浮激发的是A型波,而生产实践中一般也激发A型波。按本力学模型所进行的流场速度计算,与在水模实验中所进行的二维激光测速的实测流场相比较,其分布与数值相当一致。     

截断δ冲击模型标值过程的协方差

在自激滤过泊松过程协方差研究的基础上,推导出了截断δ冲击模型标值过程的协方差的显式表达式,拓展了δ冲击模型理论。     

机械密封对转子轴承系统动力学性能的影响

采用集总质量模型和传递矩阵法建立了考虑机械密封影响的转子轴承系统动力学方程,并采用广义逆迭代法求解出上述线性方程组的特征值.在考察系统的响应时,采用Gauss消元法计算不平衡激励下系统的强迫振动响应.结合某典型的八字形螺旋槽式液体机械密封的动特性参数计算结果,给出了机械密封对高速转子轴承系统动力学行为的影响,并同时分析了结构参数对系统动力学性能的影响,以及在不平衡激励下考虑机械密封系统时转子轴承系统的强迫振动响应.结果表明,机械密封的存在对高速转子轴承系统动力学行为有一定的影响.例如,对于柔性转子系统,考虑机械密封系统时可使系统的一阶阻尼临界转速提高60%～80%.     

Comparison of prospective Hawkes and recursive point process models for Ebola in DRC

Point process models, such as Hawkes and recursive models, have recently been shown to offer improved accuracy over more traditional compartmental models for the purposes of modeling and forecasting the spread of disease epidemics. To explicitly test the performance of these two models in a real-world and ongoing epidemic, we compared the fit of Hawkes and recursive models to outbreak data on Ebola virus disease (EVD) in the Democratic Republic of the Congo in 2018–2020. The models were estimated, and the forecasts were produced, time-stamped, and stored in real time, so that their prospective value can be assessed and to guard against potential overfitting. The fit of the two models was similar, with both models resulting in much smaller errors in the beginning and waning phases of the epidemic and with slightly smaller error sizes on average for the Hawkes model compared with the recursive model. Our results suggest that both Hawkes and recursive point process models can be used in near real time during the course of an epidemic to help predict future cases and inform management and mitigation strategies.     

自激滤过泊松过程的协方差

主要利用特征函数与协方差的关系,以及重积分的性质,得到了自激滤过的泊松过程的协方差的显示表达式。     

自激滤过的泊松过程的二阶矩

讨论了自激滤过的泊松过程的二阶矩,并将所得结论应用于截断δ冲击模型的标值过程和客户寿命价值,得到了截断δ冲击模型的标值过程的二阶矩和客户寿命价值的二阶矩。