Option pricing and perfect hedging on correlated stocks

We develop a theory for option pricing with perfect hedging in an inefficient market model where the underlying price variations are autocorrelated over a time τ0. This is accomplished by assuming that the underlying noise in the system is derived by an Ornstein-Uhlenbeck, rather than from a Wiener process. With a modified portfolio consisting in calls, secondary calls and bonds we achieve a riskless strategy which results in a closed and exact expression for the European call price which is always lower than Black-Scholes price. We obtain the same price and a modified delta hedging if we start from an effective one-dimensional market model. We compare these strategies and study the sensitivity of the call price to several parameters where the correlation effects are also observed.     

气体放电等离子体中多重随机共振实验及数值研究

在气体放电等离子体随机共振实验中观察到了信噪比随噪声强度出现多次共振的现象。这种现象与动力学系统的多稳性质相关。通过对多稳动力学系统随机共振的数值模拟，获得了与实验现象类似的随机共振曲线。     

Topics in data assimilation: Stochastic processes

Stochastic models with varying degrees of complexity are increasingly widespread in the oceanic and atmospheric sciences. One application is data assimilation, i.e., the combination of model output with observations to form the best picture of the system under study. For any given quantity to be estimated, the relative weights of the model and the data will be adjusted according to estimated model and data error statistics, so implementation of any data assimilation scheme will require some assumption about errors, which are considered to be random. For dynamical models, some assumption about the evolution of errors will be needed. Stochastic models are also applied in studies of predictability.

The formal theory of stochastic processes was well developed in the last half of the twentieth century. One consequence of this theory is that methods of simulation of deterministic processes cannot be applied to random processes without some modification. In some cases the rules of ordinary calculus must be modified.

The formal theory was developed in terms of mathematical formalism that may be unfamiliar to many oceanic and atmospheric scientists. The purpose of this article is to provide an informal introduction to the relevant theory, and to point out those situations in which that theory must be applied in order to model random processes correctly.     

Stationary optimal control of a stochastic system with stable environmental interferences

In this paper, we consider a class of nonstationary control systems. We obtain some conditions for stationary optimal controls of such systems. The results are then applied to a linear-quadratic system.     

13C direct detected COCO-TOCSY: a tool for sequence specific assignment and structure determination in protonless NMR experiments

A novel experiment is proposed to provide inter-residue sequential correlations among carbonyl spins in (13)C detected, protonless NMR experiments. The COCO-TOCSY experiment connects, in proteins, two carbonyls separated from each other by three, four or even five bonds. The quantitative analysis provides structural information on backbone dihedral angles phi as well as on the side chain dihedral angles of Asx and Glx residues. This is the first dihedral angle constraint that can be obtained via a protonless approach. About 75% of backbone carbonyls in Calbindin D(9K), a 75 amino acid dicalcium protein, could be sequentially connected via a COCO-TOCSY spectrum. 49 [Formula: see text] values were measured and related to backbone phi angles. Structural information can be extended to the side chain orientation of aminoacids containing carbonyl groups. Additionally, long range homonuclear coupling constants, (4)J(CC) and (5)J(CC), could be measured. This constitutes an unprecedented case for proteins of medium and small size.     

水声时变线谱建模与双稳态随机共振分析

建立了水声时变线谱的模型,将双稳态随机共振系统应用于水声时变线谱信号的检测,考查了随机共振系统对水声环境的适应能力,提出了设计水声线谱检测系统可以利用的外在参数。在信噪比变化、声压起伏、线谱漂移等情况下,仿真结果表明双稳态随机共振系统都能较好地工作。为水声领域新型线谱检测系统的设计提供了依据。     

自适应光学系统几种随机并行优化控制算法比较

 直接对系统性能指标进行优化是自适应光学系统中一种重要的波前畸变校正方法,选择合适的随机并行优化控制算法是该技术成功实现的关键。以32单元变形镜为校正器,基于多种随机并行优化算法建立自适应光学系统仿真模型。从算法的收敛速度、校正效果、局部极值3个方面对遗传算法、单向扰动随机并行梯度下降、双向扰动随机并行梯度下降及模拟退火算法进行了比较。仿真结果表明,遗传算法收敛速度太慢,不适用于需要实时控制的自适应光学系统;双向扰动随机并行梯度下降算法收敛速度、校正效果要优于单向扰动随机并行梯度下降,且能够适应各种情况下的扰动电压;模拟退火几乎以概率1收敛到全局极值附近,且收敛速度是上述算法中最快的。     

Escape process and stochastic resonance under noise intensity fluctuation

We study the effects of noise intensity fluctuations on the stationary and dynamical properties of an overdamped Langevin model with a bistable potential and external periodical driving force. We calculated the stationary distributions, mean-first passage time (MFPT) and the spectral amplification factor using a complete set expansion (CSE) technique. We found resonant activation (RA) and stochastic resonance (SR) phenomena in the system under investigation. Moreover, the strength of RA and SR phenomena exhibit non-monotonic behavior and their trade-off relation as a function of the squared variation coefficient of the noise intensity process. The reliability of CSE is verified with Monte Carlo simulations.     

Lyapunov control of squeezed noise quantum trajectory

The quantum trajectory renders the optimal estimation of quantum state. It is a classical Itô stochastic differential equation. The Lyapunov global stabilization problem is solved for squeezed noise quantum trajectory. Lyapunov control stabilizes the quantum system toward one eigenstate. A two-level bistable quantum system is simulated as an example.     

Analysis of distances between inclusions in finite binary stochastic materials

A generalized probability density function (PDF) describing the distribution of inter-inclusion distances in finite, isotropic, binary stochastic materials with fixed diameter inclusions has been developed and tested. The new probability density function explicitly accounts for edge effects present in finite two- and three-dimensional stochastic materials. The generalized PDF is shown to include factors that are dependent on both the geometry of the material region as well as the statistical properties of the material. A discussion of the properties and application of this newly developed PDF is provided along with supporting numerical results for case studies in one- and two-dimensions. These numerical results demonstrate the ability of the newly derived PDF to correctly account for edge effects in finite stochastic materials, while still reproducing the expected distribution within the bulk material region.