The t-distribution has a “fat tail” feature, which is more suitable than the normal probability density function to describe the distribution characteristics of return on assets. The difficulty of using t-distributi...The t-distribution has a “fat tail” feature, which is more suitable than the normal probability density function to describe the distribution characteristics of return on assets. The difficulty of using t-distribution to price European options is that a fat tail can lead to a deviation in one integral required for option pricing. We use a distribution called logarithmic truncated t-distribution to price European options. A risk neutral valuation method was used to obtain a European option pricing model with logarithmic truncated t-distribution.展开更多
Optimization algorithms play a pivotal role in enhancing the performance and efficiency of systems across various scientific and engineering disciplines.To enhance the performance and alleviate the limitations of the ...Optimization algorithms play a pivotal role in enhancing the performance and efficiency of systems across various scientific and engineering disciplines.To enhance the performance and alleviate the limitations of the Northern Goshawk Optimization(NGO)algorithm,particularly its tendency towards premature convergence and entrapment in local optima during function optimization processes,this study introduces an advanced Improved Northern Goshawk Optimization(INGO)algorithm.This algorithm incorporates a multifaceted enhancement strategy to boost operational efficiency.Initially,a tent chaotic map is employed in the initialization phase to generate a diverse initial population,providing high-quality feasible solutions.Subsequently,after the first phase of the NGO’s iterative process,a whale fall strategy is introduced to prevent premature convergence into local optima.This is followed by the integration of T-distributionmutation strategies and the State Transition Algorithm(STA)after the second phase of the NGO,achieving a balanced synergy between the algorithm’s exploitation and exploration.This research evaluates the performance of INGO using 23 benchmark functions alongside the IEEE CEC 2017 benchmark functions,accompanied by a statistical analysis of the results.The experimental outcomes demonstrate INGO’s superior achievements in function optimization tasks.Furthermore,its applicability in solving engineering design problems was verified through simulations on Unmanned Aerial Vehicle(UAV)trajectory planning issues,establishing INGO’s capability in addressing complex optimization challenges.展开更多
文摘为了解决经典缓变故障检测法——自主完好性监测外推法(autonomous integrity monitoring extrapolation,AIME)在组合导航中检测故障延迟时间较长和不能准确判定故障结束时刻的问题,提出了基于抗差估计和改进AIME的缓变故障检测方法。该方法采用标准t分布和IGG-Ⅲ(Institute of Geodesy&GeophysicsⅢ)方案设计自适应增益矩阵以缓解卡尔曼滤波故障跟踪的影响。同时,结合AIME故障检测状态,提出由外推法和残差卡方检验(residual chi-square test method,RCTM)故障检测统计量构成的r_(A/R)统计量概念,然后在AIME检测到缓变故障的状态下利用样本分位数原理对r_(A/R)序列进行异常值检测,从而判断缓变故障结束时刻。仿真结果表明,在检测缓变故障时,所提方法可明显缩短故障检测延迟时间,并能够准确判定故障结束时刻。
文摘The t-distribution has a “fat tail” feature, which is more suitable than the normal probability density function to describe the distribution characteristics of return on assets. The difficulty of using t-distribution to price European options is that a fat tail can lead to a deviation in one integral required for option pricing. We use a distribution called logarithmic truncated t-distribution to price European options. A risk neutral valuation method was used to obtain a European option pricing model with logarithmic truncated t-distribution.
基金supported by theKey Research and Development Project of Hubei Province(No.2023BAB094)the Key Project of Science and Technology Research Program of Hubei Educational Committee(No.D20211402)the Open Foundation of HubeiKey Laboratory for High-Efficiency Utilization of Solar Energy and Operation Control of Energy Storage System(No.HBSEES202309).
文摘Optimization algorithms play a pivotal role in enhancing the performance and efficiency of systems across various scientific and engineering disciplines.To enhance the performance and alleviate the limitations of the Northern Goshawk Optimization(NGO)algorithm,particularly its tendency towards premature convergence and entrapment in local optima during function optimization processes,this study introduces an advanced Improved Northern Goshawk Optimization(INGO)algorithm.This algorithm incorporates a multifaceted enhancement strategy to boost operational efficiency.Initially,a tent chaotic map is employed in the initialization phase to generate a diverse initial population,providing high-quality feasible solutions.Subsequently,after the first phase of the NGO’s iterative process,a whale fall strategy is introduced to prevent premature convergence into local optima.This is followed by the integration of T-distributionmutation strategies and the State Transition Algorithm(STA)after the second phase of the NGO,achieving a balanced synergy between the algorithm’s exploitation and exploration.This research evaluates the performance of INGO using 23 benchmark functions alongside the IEEE CEC 2017 benchmark functions,accompanied by a statistical analysis of the results.The experimental outcomes demonstrate INGO’s superior achievements in function optimization tasks.Furthermore,its applicability in solving engineering design problems was verified through simulations on Unmanned Aerial Vehicle(UAV)trajectory planning issues,establishing INGO’s capability in addressing complex optimization challenges.
