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The relationship between futures and spot is stillan important issue in academic communities and supervisory departments. Inthis paper, the Granger Causality Test is extended into quantile regressionand then the relationship between futures and spot is investigated atdifferent quantile positions. Note that under the model with differentialdata, different quantile positions are related to the corresponding financialenvironments. Consequently, a market-dependent casuality between futures andspot is established, by which we can study the relationship more deeply andcomprehensively. The main points of view obtained in this paper are whatfollows: 1. The relationship between futures and spot is strongly relatedto the financial environments, besides the features of futures and spot;2. Under the normal and stable financial markets, there is casuality oneanother, but the relationship will be abnormal under extremal financialconditions, the common relationship between futures and spot is masked byother financial factors; 3. If the casuality was seen as a normal factlogically, then the abnormal relationship should indicate a bad or extremalfinancial environment, which provides supervisory departments with a warningsignal.     

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本文在产品寿命服从双参数指数分布的无替换定数截尾寿命试验场合下,提出了两独立产品平均寿命比率的两个估计量,并研究了这两个比率估计量的渐近正态性和置信区间. 然后通过数据模拟,进一步验证了所提出比率估计量的有效性.     

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??In this paper, we investigate a robust optimal portfolio andreinsurance problem under inflation risk for an ambiguity-averse insurer (AAI), who worriesabout uncertainty in model parameters. We assume that the AAI is allowed to purchaseproportional reinsurance and invest his/her wealth in a financial market which consists ofa risk-free asset and a risky asset. The objective of the AAI is to maximize the minimalexpected power utility of terminal wealth. By using techniques of stochastic control theory,closed-form expressions for the value function and optimal strategies are obtained.     

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??This paper investigates the test of significance for the binarychoice model with stochastic trend process. The results show that when the true parametervector is zero, the limiting distribution of the t statistic follows standard normaldistribution. The joint significance test statistics Wald, LM and LR are asymptoticallyequivalent and have a Chi-square limiting distribution.     

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??In this paper we consider a class of fractional stochastic partial differential equation driven by fractional noise. We prove that the solution admits a smooth density at any fixed point (t,x)in[0,T]timesmathbb{R} with T>0 by using the techniques of Malliavin calculus.     

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A Markov observation model with dividend is defined and the interpretation of the practical significance is given. We try to use an irreducible and homogeneous discrete-time Markov chain to modulate the inter-observation times and embed a dividend strategy. In the Markov observation model with dividend, a system of liner equations for the expected discounted value of dividends until ruin time is derived. Moreover, an explicit expression is obtained and proved. Finally, some interesting properties are illustrated by numerical analysis and by comparing with the complete compound binomial model with dividend.     

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设备的平均寿命是可靠性研究中的的一个重要指标.对威布尔分布来说, 由于平均寿命没有明显的枢轴量,因此给出平均寿命的精确的置信限较为困难.本文分别利用广义枢轴量、WCF展开以及三阶法三种方法,得到了设备寿命服从威布尔分布时的平均寿命的(近似)置信下限.最后对上述三种方法分别进行了模拟比较,结果显示文中给出的方法对于中小样本情形下得到的平均寿命的置信限是比较精确的.     

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Let, be two independent,
-dimensional sub-fractional Brownian motions with respective indices.
Assume. Our principal results are the necessary and sufficient condition for the
existence and smoothness of the collision local time and the intersection local time of
and through chaos expansion and elementary inequalities.     

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In this paper, we establish the option pricing model under sub-fractional Brownian motion, and consider the situation of the continuous dividend payments. Firstly, Wick-It^{o} integral and partial differential method are used to get the option price of partial differential equation, and then through variable substitution into Cauchy problem, we can get the pricing formula of European call option with dividend-paying in sub-fractional Brownian motion environment.According to the pricing formula of European call option, the European put option pricing formula is obtained. Moreover, we study the parameter estimation in the model, and consider the unbiasedness and the strong convergence of the estimator.     

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This paper considers a dividend strategy with investment inOmega model. If at a potential dividend-payment time the surplus is above, partof the excess are paid as dividends directly, the other part are used as dynamicinvestment capital, at a particular time, the sum of profits and investment capitalwill be paid as another dividend. Under this dividend policy, we get the optimaldividend strategy and the optimal portfolio policy.     

Option pricing when the regime-switching risk is priced

We study the pricing of an option when the price dynamic of the underlying risky asset is governed by a Markov-modulated geometric Brownian motion. We suppose that the drift and volatility of the underlying risky asset are modulated by an observable continuous-time, finite-state Markov chain. We develop a two- stage pricing model which can price both the diffusion risk and the regime-switching risk based on the Esscher transform and the minimization of the maximum entropy between an equivalent martingale measure and the real-world probability measure over different states. Numerical experiments are conducted and their results reveal that the impact of pricing regime-switching risk on the option prices is significant.     

基于FFT的区域变换对数均匀跳扩散模型期权定价

本文考虑具有区域变换跳跃幅度服从对数均匀分布的跳扩散模型的期权定价问题.本文给出了这样模型的期权定价方法和计算过程,当中采用了FFT(快速傅里叶变换法),最后给出了数值计算结果.     

An Algorithm for Computing Fundamental Solutions of Difference Operators

We propose an FFT-based algorithm for computing fundamental solutions of difference operators with constant coefficients. Our main contribution is to handle cases where the symbol has zeros.     

γ-循环线性方程组的快速算法

1．引言在数学以及应用科学中的许多问题都与周期性有关,从而导致一类特殊形式的TOeelitZ系统,即r一循环线性系统的求解,其计算复杂性为O（N”）［’j或渐近复杂性O（NlogZN）p］．由于循环矩阵与离散富里时变换之间的关系,我们也可通过快速富里叶变换（＊＊n来求解r一循环线性方程组,计算复杂性降为O（NlogZN）［‘,’］．事实上,到目前为止所有与厂循环矩阵有关问题的快速算法全部建立在富里叶变换某础之卜IZ,9,10,17,19,20］但另一方面富里叶交换定义在复数域上,而实际问题中的数据大多为实数,因此用FFT快速求解r…     

A fast modified sine transform for solving block-tridiagonal systems with Toeplitz blocks

In this report we consider block-tridiagonal systems with Toeplitz blocks. Each block is of sizen×n consisting ofn _c×n _c matrices as entries, and there arem×m blocks in the system. The solution of those systems consists of 2n _c m modified sine transforms and an intermediate solution ofn block-tridiagonal systems. Symmetries in the data vectors are exploited such that one modified sine transform can be computed in terms of one Fourier transform of half the length of the original one, hence requiringO(2.5nlog₂ n) operations. Similarly, we only have to solve (n+1)/2 of the intermediate systems due to symmetry.This work was supported by the Swedish National Board for Industrial and Technical Development, NUTEK, under contract No. 89-02539 P.     

基于机制转换跳扩散模型的外汇挂钩的相关期权定价

本文研究了机制转换跳扩散模型下外汇挂钩的相关期权的定价问题. 在风险中性概率测度下,假设汇率服从机制转换均值回复模型、资产价格服从机制转换跳扩散模型,通过测度变换和傅里叶变换方法, 推导出了外汇挂钩相关期权的定价公式.运用快速傅里叶变换算法求得期权价值的数值解,并比较分析了不同模型以及一些重要参数对外汇挂钩相关期权价值的影响情况.