α-times Integrated Regularized Cosine Functions and Second Order Abstract Cauchy Problems

In this paper, a -times integrated C-regularized cosine functions and mild a -times integrated C-existence families of second order are introduced. Equivalences are proved among a -times integrated C-regularized cosine function for a linear operator A, C-wellposed of (a + l)-times abstract Cauchy problem and mild a -times integrated C-existence family of second order for A when the commutable condition is satisfied. In addition, if A = C~1AC, they are also equivalent to A generating the a -times integrated C-regularized cosine function. The characterization of an exponentially bounded mild a -times integrated C-existence family of second order is given out in terms of a Laplace transform.     

双障碍期权的定价问题

根据初始股票价格S0的位置将双障碍期权划分为两大类,研究了双障碍期权的定价问题,发现双障碍期权或由一份单障碍期权和一份双边敲出期权组合而成或由两份单障碍期权组合而成,从而将双障碍期权的定价问题转化为单障碍期权和双边敲出期权的定价问题.     

随机利率下两类重置期权的定价公式

假设市场利率服从Vasicek模型.用PDE方法讨论了随机利率下两类重置期权的定价问题,建立它们的定价模型并得到了相应的解析表达式.     

随机波动率下的脆弱期权定价问题

考虑含有交易对手违约风险的期权定价.在随机波动率情况下,采用PDE方法对脆弱期权进行建模,并且推导出定价方程.然后利用有限差分方法给出数值解法,并对数值结果和参数进行了分析.     

α-times Integrated Regularized Cosine Functions and Second Order Abstract Cauchy Problens

In this paper, α -times integrated C-regularized cosine functions and mild α-times integrated C-existence families of second order are introduced. Equivalences are proved among α -times integrated C-regularized cosine function for a linear operator A, C-wellposed of (α + 1)-times abstract Cauchy problem and mild α -times integrated C-existence family of second order for A when the commutable condition is satisfied. In addition, if A = C-1AC, they are also equivalent to A generating the α -times integrated C-regularized cosine finction.The characterization of an exponentially botnded mild α -times integrated C-existence family of second order is given out in terms of a Laplace transform.     

重置期权的创新及其定价问题

结合回望期权的买入按低价,卖出按高价的特点对重置期权进行创新.应用最高与最低原生资产价格的概率分布得出了一类创新重置看涨期权、看跌期权的定价公式.     

微分方程x=φ(y)-F(x),y=-g(x)存在中心的判别准则

利用奇点理论和变换研究微分方程中心的存在性,给出了两个判别准则。     

关于Liénard方程存在极限环的两个定理

本文我们利用Hopf分支定理给出了Liénard方程存在极限环和两个推广的判别准则。