Analytic solutions for optimal statistical arbitrage trading

In this paper we derive analytic formulae for statistical arbitrage trading where the security price follows an Ornstein-Uhlenbeck process. By framing the problem in terms of the first-passage time of the process, we derive expressions for the mean and variance of the trade length and the return. We examine the problem of choosing an optimal strategy under two different objective functions: the expected return, and the Sharpe ratio. An exact analytic solution is obtained for the case of maximising the expected return.     

Iterative proximal regularization of the modified Lagrangian functional for solving the quasi-variational Signorini inequality

The iterative Uzawa method with a modified Lagrangian functional is used to numerically solve the semicoercive Signorini problem with friction (quasi-variational inequality).     

Global asymptotic stability of solutions of a functional integral equation

Using the technique of measures of noncompactness we prove a theorem on the existence and global asymptotic stability of solutions of a functional integral equation. The investigations are placed in the Banach space of real functions defined, continuous and bounded on an unbounded interval. A few realizations of the result obtained are indicated.     

Fractional Lévy processes on Gel’fand triple and stochastic integration

In this paper, we investigate the long-range dependence of fractional Lévy processes on Gel’fand triple and construct stochastic integral with respect to fractional Lévy processes for a class of deterministic integrands.      

关于伪压缩映象不动点迭代的一点注记

设$K$是自反的并且具有一致Gateaux可微范数的Banach空间$E$的非空有界闭凸子集.设$T:K\rightarrow K$是一致连续的伪压缩映象.假设$K$的每一非空有界闭凸子集对非扩张映象具有不动点性质.设$\{\lambda_n\}$是$(0,\frac{1}{2}]$中序列满足: (i) $\lim_{n\rightarrow \infty}\lambda_n=0$; (ii) $\sum_{n=0}^{\infty}\lambda_n=\infty$.任给$x_1\in K$,定义迭代序列$\{x_n\}$为:$x_{n+1}=(1-\lambda_n)x_n+\lambda_nTx_n-\lambda_n(x_n-x_1),n\geq 1.$若$\lim_{n\rightarrow \infty}\|x_n-Tx_n\|=0$, 则上述迭代产生的$\{x_n\}$强收敛到$T$的不动点.     

渐近φ伪压缩映象有限族的迭代程序的强收敛(英文)

Strong convergence theorems for approximation of common fixed points of asymptoticallyφ-quasi-pseudocontractive mappings and asymptoticallyφ-strictly- pseudocontractive mappings are proved in real Banach spaces by using a new compos- ite implicit iteration scheme with errors.The results presented in this paper extend and improve the main results of Sun,Gu and Osilike published on J.Math.Anal. Appl.     

二阶共振周期边值问题多解的存在性

借助于与给定共振的非线性周期边值问题相关的非共振的线性边值问题来构造算子,利用范数形式的锥拉伸-压缩不动点定理,得到了非线性周期边值问题非负解的存在性定理.     

Iterative convergence theorems for maximal monotone operators and relatively nonexpansive mappings

In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.     

MULTIPLE POSITIVE SOLUTIONS TO SOME SECOND-ORDER m-POINT BOUNDARY VALUE PROBLEMS

Multiplicity of positive solutions to some second order m-point boundary value problems are considered. By fixed-point theorems in a cone, some new results are obtained. The associated Green’s function of these problems are also given.