The pricing formula of stock option with the rules of limit up and limit down

借鉴MErTOn的跳跃扩散模型的思想,根据中国股市的具体情况,用含有POISSOn过程的ITO-SkOrOHOd随机微分方程描述股票价格的运动.利用鞅定价技巧(风险中性方法)推导出考虑涨跌停规则的跳跃扩散的股票期权在T时刻的价格公式,并利用随机模拟和中心极限定理讨论如何具体计算股票期权的价格.Based on the idea of jump and pervasion by Merton,a model for underlying asset price with a diffusion process involving jump and pervasion was established.By applying Ito-Skorohod formula and martingale pricing sleight within the framework of our model,a closed form analytic solution for the pricing formula of stock option with the rules of limit up and limit down was derived.Then,the idiographic forms on the different circumstances by stochastic simulation and center limit theorem is discussed.国家自然科学基金资助项目(11001142;10671103

Dynamics model in the system of Tessaratoma papillosa-parasitoid wasp and its application

研究荔枝蝽 -寄生蜂系统的数量变动规律 ,得到一个差分 -积分方程组及求解的递推公式 ,指出了公式中参数的确定方法。推导出荔枝蝽 -寄生蜂系统长期演变的特性 ,用模型证明了人工放蜂防治荔枝蝽的优越性及滥用农药的不良后果 ,给出了人工放蜂的最佳次数 ,最佳时刻及合适的放蜂量的计算公式 ,导出的结论与实验结果相符It is well known that Anastatus sp. and Ooencyrtus sp. are effective in killing Tessaratoma papillosa .So it is important to investigate the population dynamics in parasitoid wasp Τessaratoma papillosa system and to develop strategy of releasing of artificially reared parasitoid to the field.It is a common method to predicate the current pest quantity by its last generation dynamics combining with the analysis of environment factors. Different generations of Tessaratoma papillosas can be easily distinguished but that of parasitoid wasps would not be done. In fact, it is quite difficult to check which generations the parasitoid wasps should belong to.Thus we could not describe exactly the population of parasitoid wasp Tessaratoma papillosa by only differential or difference equations. A coupled equations consisting of both differential equation and difference equation modeling Tessaratoma papillosa parasitoid wasp interaction is necessary. A difference integral equation model for Tessaratoma papillosa parasitoid wasp system using the Lotka Volterra equation and a recurrence formula for solving the equation are presented in this paper. We modelled the population dynamics with the following coupled equations. Let X i (t) denote the egg number of new generation of Tessaratoma papillosa at time t of the i 'th year in a certain space (0≤ t≤T), i =1, 2,3…. The function X 1 (t) (0≤t≤T )can be obtained by fitting actual data. Using Y 1(t) to figure the amount of parasitoid wasps at time t (0≤t≤T) of the i 'th year ( i =1, 2,…) within the same space. Suppose Y i (0) is the number of parasitoid at time 0 of the i 'th year. According to the Lotka Volterra equation, we have dY\-1(t)dt=Y\-1(t)[-α+βX 1(t)] (0≤t≤T) where both α and β are two positive constants.Since X 1 (t) and Y 1 (0) are known, we have Y 1(t)=Y 1(0)e ∫ t o[-α+βX 1(σ)] d σ ,(0≤t≤T) Let k be the average parasitism rate per parasitoid. We use X 1(t)=X 1(t)-kY 1=X 1(t)-kY 1(o)e ∫ t 0[-α+βX 1(σ)] d σ to denote the amount of pest eggs which are not parasitoid in the first year and suppose they can all grow up and lay eggs, where λ serve as the average ovipositor quantity per adult pest. Thus we have: X 2(t)=λX 1(t)=λ[X 1(t)-kY 1(t)]=λX 1(t)-λkY 1(0)e ∫ t 0[-α+βX 1(σ)] d σ Inductively, we obtain the following model:X n(t)=λ[X n-1 (t)-kY n-1 (t)] Y n(t)=Y 1(o)n-1 i=1e ∫ t 0[-α+βX i(σ)] d σ e ∫ t 0[-α+βX n(σ)] d σ (1)Using the integral difference equations above,we can predicate the number of the pest eggs and parasitoid at time t of each year by means of recurrence. The parameter κ , denoting the average number of porosities eggs per parasitoid, is transformed from mean ovipositor number per parasitoid combined with parasitism rates, and λ , denoting the average fecundity value per pest, which can be determined from laboratory rearing experiment respectively. Parameter α and β are confirmed based on model (1), one can obtain. ln (y n(0)/y n-1 (0))=-αT+β∫ T 0x n-1 (σ) d σ (n=1,2,3,…) where ∫ T 0X n(σ) d σ is the ovipositor amount of the pest during the n 'th year. When the amount of pest ovipositor in the i 'th year and the amount of parasitoid wasps at time 0 in the corresponding year, namely ∫ T 0X i(σ) d σand Y i (0), ( i =1,2,… m ) are known, we can obtain the parameters of α and β by linear regression. Long term dynamic characterization of the system is deduced base on the model. In Model (1), assume t=T . Then it follows: X n(T)=λ[X n-1 (T)-kY n-1 (T)] Y n(T)=Y 1(O)ni=1e ∫ T 0[-α+βX i(σ)] d σ (2)when n →∞, Y n(t) becomes a infinite product. We get the following results by using the infinite product theory: Proposition 1 The prerequisi

Credit risk of the foreign stock option with the stochastic exchange rate

在结构化模型下,考虑标的资产价格与该资产所属企业的企业价值以及汇率均为随机的情况,对一类外国股票期权分别用内币执行价和外币执行价进行了信用风险分析,并采用鞅方法得到了不确定汇率下的该类外国股票期权的信用风险定价.On the hypothesis of underlying asset price,enterprise value and exchange rate were stochastic,we re-searched the method of how to analyze the credit risk of the foreign stock option by the strike price with foreign cur-rency and inland currency.By applying the method of structural approach,we derived the pricing formulas of default option with stochastic exchange rate.国家自然科学基金(11001142); 福建省教育厅科学研究项目(JB11173;JB12171); 莆田学院教育教学改革项目(JG201112

类泛素蛋白及其中文命名

泛素家族包括泛素及类泛素蛋白,约20种成员蛋白.近年来,泛素家族领域取得了迅猛发展,并已与生物学及医学研究的各个领域相互交叉.泛素家族介导的蛋白质降解和细胞自噬机制的发现分别于2004和2016年获得诺贝尔奖.但是,类泛素蛋白并没有统一规范的中文译名. 2018年4月9日在苏州召开的《泛素家族介导的蛋白质降解和细胞自噬》专著的编委会上,部分作者讨论了类泛素蛋白的中文命名问题,并在随后的\"泛素家族、自噬与疾病\"(Ubiquitinfamily,autophagy anddiseases)苏州会议上提出了类泛素蛋白中文翻译草案,此草案在参加该会议的国内学者及海外华人学者间取得了高度共识.冷泉港亚洲\"泛素家族、自噬与疾病\"苏州会议是由美国冷泉港实验室主办、两年一度、面向全球的英文会议.该会议在海内外华人学者中具有广泛影响,因此,参会华人学者的意见具有一定的代表性.本文介绍了10个类别的类泛素蛋白的中文命名,系统总结了它们的结构特点,并比较了参与各种类泛素化修饰的酶和它们的生物学功能.文章由45名从事该领域研究的专家合作撰写,其中包括中国工程院院士1名,相关学者4名,长江学者3名,国家杰出青年科学基金获得者18名和美国知名高校华人教授4名.他们绝大多数是参加编写即将由科学出版社出版的专著《泛素家族介导的蛋白质降解和细胞自噬》的专家

A Dynamic Model of Insects' Population With T-dependent Rate of Increase, Migration, Fluctuate and A Method to Determine the Minimum Cost of Preventing Pests by Using The Pests' Natural Enemy

用回归方法确定种群数量增长率、迁移率与波动率的最优拟合曲线,求解带时变漂移串与波动串的IT(？)随机微分方程,建立有迁移行为的害虫种群的数量变动模型,进而给出确定生物防治最小成本的计算方法,指出了确定模型中参数的统计方法。A dynamic model of insects' population with migration acting was evaluated by solving Ito stochastic differential equation with t-deperident rate of increase and fluctuate, a formula to determine the minimum cost of preventing pests by using the pests' natural enemy was proposed , the statistical methods to get the optimal fitting curve for the insects' population's increasing rate, migrating rate, fluctuating rate and to determine the parameters in the model was pointed out

The Optimal Threshold and Moment for Preventing The Random Walking Insect's Population

以随机过程为数学工具,用金融风险管理的思想,研究随机波动的害虫种群对作物造成的损失和药物防治费用之间的关系,依据最优经济效益原则确定害虫的最优防治阈值与防治时刻.The relation between crop's cost and insecticide cost for preventing the random walking insect's population was found by means of the theory of stochastic processes and the idea of managed financial risk, the formula to determining the optimal threshold and moment for preventing insects was gained based on the economical optimal principle

A Mathematical Method to Determine Optimal Raising Quantity of Pests' Natural Enemy

以ITO随机微分方程为工具，研究了昆虫种群因环境因素变化产生随机波动情况下的数量变化规律；利用求极小值的方法，给出了生物防治中确定天敌最佳饲养数量的计算公式，指出了确定公式中参数的统计方法。A dynamic model of pests' population's quantity with random rise and fall as the environment varying was evaluated by using the methods of Ito stochastic differential equations, a formula to determine optimal raising quantity of pests' natural enemy for biological control was proposed by using the method of finding minimal value, the statistical method to determine the parameters in the formula was pointed out

A Formula of the Distribution Density of Waiting Time for a Class of Doubly Stochastic Poisson Process and It's Application in Forecasting Insects

对具有强度过程λt(X)＝XαV(t)(α∈R+)生随机Poisson过程{Nt：t≥t0}，推导出其等待时间Wn的分布密度函数fWn(t)的表式；讨论了进一步推广所得结果的途径；利用所得结果解决了一个预测害虫最适防治时刻的问题．In this paper, a formula of distribution density function fwn (t) of waiting time for the doubly stochastic poisson process {Nt：t≥t0} with intensity process λt(X)＝XαV(t)(α∈R+) is deduced, the way to extend the results is discussed and the problem of forecasting the optimal time of preventing pests is solved by applying the results acquired

An Approximate Price Formula of Defaultable Bond with Stochastic Volatility

在假设标的资产价格的波动率是一个快速均值回复OU过程的函数的条件下,导出相应的可违约债券价格公式所应满足的偏微分方程,并利用Taylor级数展开得到一组Poisson方程.求解这些方程,得到非完全市场下固定补偿率的债券价格的近似表达式,然后在不同的补偿率规定上作了一些修正和推广.In this paper, we will establish a Credit-Risky model assuming that the volatility of the underlying risky asset price is a function of the fast mean-reverting OU process. Then, we can derive a partial differential equation to price a defaultable zero-coupon bond according to it. Furthermore we will derive an approximate solution of this equation as the price formula of defaultable bond under the incomplete market by using Taylor series expansion and the methods of solving Poisson equation. At last, we will generalize the result to a different payment function

The Application of Doubly Stochastic Poisson Process in Credit Risk Intensity Models

运用带随机尺度因子的重随机Poisson过程描述信用衍生产品的违约可能 ,在违约强度λ(t)是随机变量的情况下得到违约时间τ的分布密度函数 ,并推导出信用衍生产品的定价模型In this paper, a doubly stochastic poisson process with intersity process λ(t)=X×y(t) is used to describe the process of default. We obtain the distribution density function of default time and the solution of this intensity models.教育部优秀青年教师资助项