随机波动率模型的最小熵鞅测度和效用无差别定价

本文研究了随机波动率模型的最小熵鞅测度和效用无差别定价.利用动态规划方法,得到了效用无差别定价满足的偏微分方程以及效用无差别套期保值策略.利用指数效用函数的最优投资策略与最小熵鞅测度之间的关系,证明了最小熵鞅测度的存在性,并利用偏微分方程给出了最小熵鞅测度.     

多维系统优化中马氏田口强相关问题研究

对传统马氏田口方法进行了介绍,分析了多维系统马氏田口优化中强相关问题的影响,提出了解决强相关问题的新方法——马氏田口M-P广义逆矩阵法。相对于传统的马氏田口逆矩阵法,马氏田口M-P广义逆矩阵法具有存在性、唯一性和通用性的优点,能更有效地应用于多维系统的优化实践。通过对某医院血粘度诊断系统的优化与分析,进一步证实了马氏田口M-P广义逆矩阵法的有效性。     

体制转换下等价鞅测度的构造研究

体制转换资产价格模型可以描述宏观经济的影响,但在金融衍生产品定价所涉及的等价鞅测度的构造问题中,利用传统的Esscher变换方法得到的等价鞅测度实质上只考虑了微观市场风险,而没有考虑体制转换所表示的宏观经济风险.此外,经典的几何布朗运动不能刻画资产收益率的尖峰厚尾现象.本文首先利用马尔科夫过程和最大化非广延熵分布建立了一个新的资产价格模型.该模型可以同时描述体制转换和尖峰厚尾现象.然后利用鞅理论,借助微观市场的资产价格过程和宏观经济的马尔科夫过程的乘积给出了一种新的等价鞅测度构造方法,通过该方法构造的等价鞅测度包含了微观市场和宏观经济两种风险.最后,在该等价鞅测度下,给出了资产价格折现过程为鞅的充要条件,为进一步研究金融衍生产品的定价及风险控制提供了理论基础.     

H－值鞅测度的表示定理

研究了Ｈｉｌｂｅｒｔ值鞅测度的表示定理，并在一定条件下，证明了任一连续的Ｈｉｌｂｅｒｔ值正交鞅测度可以表示为Ｈｉｌｂｅｒｔ值Ｇａｕｓｓ鞅测度经时间变换后所得鞅测度的随机积分     

H—值鞅测度的表示定理

研究了Ｈｉｌｂｅｒｔ值鞅测度的表示定理，并在一定条件下，证明了任一连续的Ｈｉｌｂｅｒｔ值正交鞅测度可以表示为Ｈｉｌｂｅｒｔ值Ｇａｕｓｓ鞅测度经时间变换后所得鞅测度的随机积分。     

关于集值逆上鞅收敛性的若干结果

给出了集值逆上鞅的一些结论,在此基础上研究了集值逆上鞅在Kuratowski-Mosco收敛意义下及弱收敛意义下的收敛性.     

关于一类两指标鞅的随机积分

本文定义了有界可料过程对二指标L(log~+L)~3有界鞅的随机积分,并证明了有界可料过程对L(log~+L)~3有界鞅的随机积分是一个L(log~+L)有界鞅。     

股票价格遵循指数O-U过程的最大值期权定价

讨论了股票价格过程遵循指数O-U过程的变异期权定价问题。利用Girsanov定理获得了指数O-U过程模型的唯一等价鞅测度。利用期权定价的鞅方法,得到了离散时间最大值期权和虹式期权的定价公式。     

一个关于半鞅SDE解的不爆炸条件

讨论了与随随机测度分解半鞅对应的随机微分方程，在给出的“增长条件”下，得到了方程解的不爆炸性质。     

两参数连续鞅型随机微分方程解的轨道唯一性

设M.A分别为R_+~2=[0,∞)×[0,∞)上的两参数连续4次可积强鞅和2次可积连续适应增过程,Z是R_+~2的边界R_+~2上定义的两参数随机过程.考虑鞅型随机微分方程. 本文利用单参数半鞅Ito′s公式得到了重积分形式的两参数半鞅Ito′s公式.在此基础上,α,β满足此Lipschitz条件更弱的条件下,证明了鞅型随机微分方程解的轨道唯一性成立。     

充气膜结构零应力态求解

充气膜结构分析全过程包括9个状态和7个分析过程,零应力态是结构分析与设计的基础,将结构数值分析态和实际物理态有机联系起来。该文首次提出了一种从弹性平衡态到零应力态的逆解析数值分析方法,非线性协调矩阵广义逆法。首先,用膜线单元模拟膜面,将膜结构转化成为网格结构,由弹性平衡态预张力和材料参数,计算膜线无应力长度和伸长量;然后,基于杆系结构平衡矩阵理论和小变形假定,建立体系的协调方程,由协调矩阵M-P广义逆求解节点位移,逆向叠加求出新状态位形。根据新位形计算膜线张力向量和节点不平衡力向量,迭代求解零应力态。根据该算法,用MATLAB编制了计算程序。算例分析验证了该方法的正确性和高效性。该文对充气膜结构设计具有重要理论意义和实际指导价值。     

基于频响函数求逆法的双层圆柱壳体速度场重构

从双层圆柱壳体结构水下噪声实时预报出发,基于在内壳体上布置大量传感器来监测壳体噪声的工程方法,提出了双层圆柱壳体表面速度场实时重构方法。先试验测量到不同工况下内、外壳振动频响函数,并用H4方法进行估计,再用频响函数求逆法得到内、外壳体响应间的振动传递率矩阵。实际应用时,根据内壳体上有限测点的信号实时重构出当前工况下的外壳体表面速度场,为水下噪声的实时计算提供输入。大型舱段模型试验验证表明该方法现实可行,重构出来的外壳体速度场能满足水下噪声实时预报要求。     

A stochastically evolving non-local search and solutions to inverse problems with sparse data

Building on a martingale approach to global optimization, a powerful stochastic search scheme for the global optimum of cost functions is proposed using change of measures on the states that evolve as diffusion processes and splitting of the state-space along the lines of a Bayesian game. To begin with, the efficacy of the optimizer, when contrasted with one of the most efficient existing schemes, is assessed against a family of N_p-hard benchmark problems. Then, using both simulated and experimental data, potentialities of the new proposal are further explored in the context of an inverse problem of significance in photoacoustic imaging, wherein the superior reconstruction features of a global search vis-à-vis the commonly adopted local or quasi-local schemes are brought into relief.     

Effect of phosphate and bicarbonate replacers on quality changes of raw and cooked Pacific white shrimp as influenced by the repeated freeze–thawing

The effect of different soaking solutions and varying numbers of freeze–thaw cycles on the quality of raw and cooked Pacific white shrimp was investigated. The soaking solutions included 1) 0.75% NaOH, pH 11.5 (alkaline soaking solution; ASS), 2) ASS with 3% monosodium glutamate (pH 11.5) (ASS + 3% MSG) and 3) 2.5% NaCl containing mixed phosphates (M-P). Higher protein solubility was observed in raw shrimp treated with ASS + 3% MSG, compared with other treatments (P < 0.05), regardless of the number of freeze–thaw cycles. Raw shrimp treated with ASS + 3% MSG or M-P showed the lowest drip loss after 5 freeze–thaw cycles. No α-glucosidase (AG) or β-N-acetyl-glucosaminidase (NAG) activities were found in the raw shrimp treated with ASS + 3% MSG and M-P at all freeze–thaw cycles tested. As more freeze–thaw cycles were applied, the a*-value (redness) of raw shrimp increased (P < 0.05), while the a* value of cooked shrimp treated with ASS containing 3% MSG decreased (P < 0.05). The shear force of both raw and cooked shrimp with all treatments increased when freeze–thaw cycles increase up to 3 cycles (P < 0.05); however, it drastically decreased after 5 freeze–thaw cycles (P < 0.05). Therefore, treatment of shrimp with 0.75% NaOH containing 2.5% NaCl and 3% monosodium glutamate (pH 11.5) could retard the deteriorative change induced by freeze–thawing process.     

Linear systems driven by martingale noise

A method is developed for calculating second moment properties and moments of order three and higher of the state X of a linear filter driven by martingale noise. The martingale noise is interpreted as the formal derivative of a square integrable martingale with continuous samples. The Gaussian white noise is an example of a martingale noise. It is shown that the differential equations of the mean and correlation functions of the state X developed in the paper resemble the corresponding equations of the classical linear random vibration and coincide with these equations if the input is a Gaussian white noise. The moment equations are derived by (1) the Itô formula for semimartingales and (2) the classical Itô formula applied to a diffusion process whose coordinates include X. An advantage of the second method is use of more familiar concepts. However, this method requires to calculate unnecessary moments and can be applied only for a class of martingale noise processes. Examples are presented to illustrate and evaluate the two methods for calculating moments of X and demonstrate the use of these methods in linear random vibration.     

随机利率情形下的多维Black-Scholes模型

利用随机微分方程和鞅方法,讨论了随机利率情形下的多维Black-Scholes定价模型,并得到随机利率情形下的欧式期权以及交换期权定价公式。     

参数依赖于时间的复合期权

本文主要研究了参数依赖于时间的复合期权。通过Girsanov定理和鞅表示方法,得到欧式未定权益的复合期权定价公式及其套期保值策略。     

利率和股票价格遵循O-U过程的再装期权定价

根据再装期权的定义,对股票价格遵循指数O-U过程,利率服从O-U过程的金融市场,利用鞅工具和随机分析方法,得出了单再装日期权的定价公式,并推广到多再装日情形。