世界数学家大会(2002)卫星会议会讯

International Congress of Mathematical Software. Beijing. Aug. 1719.Contast:xgao@mmrc. iss. ac. cn; zliu@mmrc. iss. ac. ca. Wibsite: http: / /www. mathsoftware.org/Operator Algebras and Applications. Chengde. Aug.14-18.Contact: chengde@O AinChina. org; hxlin@cartan. uoregon. edu. Website: http: / /www. O AinChina. orgDifferential Geometry and Global Analysis. Tianjin. Aug.17-18.Contact: weiping@sun. nankai .edu. cnMathematical Biology Guilin. Aug.15-18.Contact: gxnu@public. glptt. …     

数学谜语

‘.，-‘.甲-鑫V-‘.，.么甲-‘.丫.血甲-主下.盛甲-五甲‘1.田. 2.安定才能团结. 3.先前太贵. (以上各打一数学名词) 4.基础不好. (打三个数学名词) 1.重心. 2.平方和. 3.近似值. 4.根、底、差数学谜语@文广!北京~~     

数学名词谜语

1 .垂钓　　　　　 2 .客运规则　　　 3 .附则　　　　　 4.八刀　　　　　　 5 .对症下药6.我有一毛钱　 7.待命出发　 8.二牛打架　 9.五角钱一回　 1 0 .找工作1 1 .双双过磅　 1 2 .考试舞弊　 1 3 .五角钱　 1 4.五四三二一(答案在本期内找 )数学名词谜语答案1 .等于 (鱼 )　　　　 2 .乘法　　　　 3 .加法　　　　　 4.分解　　　　　 5 .开方6.余角 7.等差　　 8.对顶角　　 9.一元二次　　 1 0 .求值　　1 1 .对称 1 2 .假分数　　 1 3 .半圆　　 1 4.倒数数学名词谜语…     

Coordinate Graphs

Some bars may involve many Pairs of numbers.A bar for eaeh pair would take up too mueh spaee.CoordinategraPhs are used instead.ExamPleBelow 15 a table of temPeratures for a eold January morning in Minneapolis.Put this information onto a eoordinategraPh. Time of day TemPerature(。F) 1 A.M.一2 2 A.M.一2 3 A.M.一2 4 A.M.一1 5 A.M.O 6 A.M.3 7 A.M.一1 8 A.M.O 9 A.M.3 10 A.M.7 1 1 A.M.11 12 noon 18SolutionThis eoordinate graph 15 based on two number lines.The horizontal number line r…     

GEOMETRIC CONSTRUCTION OF ASSOCIATIONSCHEMES FROM DEGENERATE QUADRICS INPROJECTIVE SPACES PG(2ν δ ι-1, Fq) FOR q ODD

1IntroductionThegeometryofquadricsandHerntitianvarietiesinfinite-dimensionalprojectivespaceshasbeenstudiedbyE-J.F.Primrose[6],D.K.tw-Chaudhuri['l8],I.M.Chakravarti["'],andR.C-BoseandI-M-Ch.kravarti[1].Inl993,I.M.Chak.ava,ti[4]derivedsomeassociationschemesandcodesfromuondegenerateHerndtia-nvarieties.In[1o],weconstructedsomedriiliesofassociationschemesfromthesetofisotropicpointsinpseudo-symplecticspaces.Inthispaper5weconsiderdegenerateqlledricsandconstructafamilyoffour-classassociations…     

Geometric construction of some families of two-class and three-class association schemes from nondegenerate quadrics in characteristic two

1.IntroductionThetheoryoflinearspacesintriteprojectivegeometryhasbeenusedbyseveralauthorsinconstructingBIBandPBIBdesigns.BoseI21firstusedthepropertiesofquadricsurfaCesinfiniteprojectivegeometryoftwoandthreedimensionsforconstr-netingexperimelltaldesigns.D.K.Ray-Chaudhurils]usedthegeometryofquadricstoconstructseveralseriesofPBIBdesignswithtwoassociateclasses.I.M.Chakravartila]usednondegenerateanddegenerateHebotianvarietiestoconstructsomefamiliesoftwo-classandthree-classassociationschemes…     

Fuzzy Ordered Filters in Implicative Semigroups

Animplicativesemilatticeisanalgebraicsystemhavingasmodelslogicalsystemsequippedwithimplicationandconjunction,butnotpossessingadisjunction.ImplicativesemilatticeswerestudiedbyW.C.Nemitz[5].In[2],T.S.BlythgeneralizedsomeresultsofW.C.Nemitz[5]byintroducingthenotionofaBrouweriansemigroup.FollowingtheideasofNemitzandBlyth,M.W.ChanandK.P.Shum[3]introducedthenotionofnegativelypartiallyorderedimplicativesemigroupsandgeneralizedsomeresultofNemitzonimplicativesemilatticestoim-plicativesemigroups…     

多变点过程的随机控制

用鞅论方法来研究多变点过程及其随机控制已引起人们注意。P.Bremaud在这方面作了许多工作.A.F.Martins-Neto与E.Wong用鞅论方法研究了排队问题.R.Boel与 P.P.Varaiya在 1977年的一篇文章中讨论了一个较为一般的跳过程最优控制模型.M.H.A.Davis与R.J.Elliott对[3]的工作作了改进,建立了跳过程最优控制的极小值原理.R.Rishel,S.R.Pliska等人用不同的方法得到类似结果.     

IMO 1991 Problems

IMO 1991washeldinSigtuna ,Sweden .· 5 5termswererepresented .·TheodorBanicaearnedhisthirdgoldmedalforRomania .·EvgenijaMalinnikovaearnedherthirdgoldmedalfortheU .S .S .R .Sheistheonlyfemalecom petitortohaveearnedthreegoldmedals.Problem1.GivenatriangleA…     

PHANTOM MAPS AND SPACES OF THE SAME n-TYPE FOR ALL n

1.IntroductionLetXbeaconnectedCWcomplexandX.denoteitsn-skeleton.Amapf:X-YiscalledaphantommapifitsrestrictiontoeachskeletonXuisnullhomotopic.ItiseasytoknowthateveryphantommapfromafiniteCWcomplexortoaspacewithonlyfinitenootrivialhomotopygroupsisnecessarilytrivialuptohomotopy.HenceessentialphantommapcanoccuronlywhenthedomainXisaninfinitedimensionalspaceorthetargetisaspacewithinfinitenontrivialhomotopygroups.Suchmapsappeartobenullhomotopicfromanumberofdifferentpoilltsofview;e.g.,theyinducethe…     

The pricing of Asian options under stochastic interest rates

The purpose of this paper is to analyse the effect of stochastic interest rates on the pricing of Asian options. It is shown that a stochastic, in contrast to a deterministic, development of the term structure of interest rates has a significant influence. The price of the underlying asset, e.g. a stock or oil, and the prices of bonds are assumed to follow correlated two-dimensional Itô processes. The averages considered in the Asian options are calculated on a discrete time grid, e.g. all closing prices on Wednesdays during the lifetime of the contract. The value of an Asian option will be obtained through the application of Monte Carlo simulation, and for this purpose the stochastic processes for the basic assets need not be severely restricted. However, to make comparison with published results originating from models with deterministic interest rates, we will stay within the setting of a Gaussian framework.     

The pricing of vulnerable options with double Mellin transforms

Many options traded in the over-the-counter markets are subject to default risks resulting from the probability that the option writer could not honor its contractual obligations. There have been growing concerns about financial derivatives subject to default risks, in particular, since the Global Financial Crisis and Eurozone crisis. This paper uses double Mellin transforms to study European vulnerable options under constant as well as stochastic (the Hull–White) interest rates. We obtain explicitly an analytic closed form pricing formula in each interest rate case so that the pricing of the options can be computed both accurately and efficiently.     

Pricing long-dated insurance contracts with stochastic interest rates and stochastic volatility

We consider the pricing of long-dated insurance contracts under stochastic interest rates and stochastic volatility. In particular, we focus on the valuation of insurance options with long-term equity or foreign exchange exposures. Our modeling framework extends the stochastic volatility model of Schöbel and Zhu (1999) by including stochastic interest rates. Moreover, we allow all driving model factors to be instantaneously correlated with each other, i.e. we allow for a general correlation structure between the instantaneous interest rates, the volatilities and the underlying stock returns. As insurance products often incorporate long-term exposures, they are typically more sensitive to changes in the interest rates, volatility and currencies. Therefore, having the flexibility to correlate the underlying asset price with both the stochastic volatility and the stochastic interest rates, yields a realistic model which is of practical importance for the pricing and hedging of such long-term contracts. We show that European options, typically used for the calibration of the model to market prices, and forward starting options can be priced efficiently and in closed-form by means of Fourier inversion techniques. We extensively discuss the numerical implementation of these pricing formulas, allowing for a fast and accurate valuation of European and forward starting options. The model will be especially useful for the pricing and risk management of insurance contracts and other exotic derivatives involving long-term maturities.     

Pricing long-dated insurance contracts with stochastic interest rates and stochastic volatility

We consider the pricing of long-dated insurance contracts under stochastic interest rates and stochastic volatility. In particular, we focus on the valuation of insurance options with long-term equity or foreign exchange exposures. Our modeling framework extends the stochastic volatility model of Schöbel and Zhu (1999) by including stochastic interest rates. Moreover, we allow all driving model factors to be instantaneously correlated with each other, i.e. we allow for a general correlation structure between the instantaneous interest rates, the volatilities and the underlying stock returns. As insurance products often incorporate long-term exposures, they are typically more sensitive to changes in the interest rates, volatility and currencies. Therefore, having the flexibility to correlate the underlying asset price with both the stochastic volatility and the stochastic interest rates, yields a realistic model which is of practical importance for the pricing and hedging of such long-term contracts. We show that European options, typically used for the calibration of the model to market prices, and forward starting options can be priced efficiently and in closed-form by means of Fourier inversion techniques. We extensively discuss the numerical implementation of these pricing formulas, allowing for a fast and accurate valuation of European and forward starting options. The model will be especially useful for the pricing and risk management of insurance contracts and other exotic derivatives involving long-term maturities.     

A mathematical model of pricing in a large system of cash bonds

The purpose of this paper is to give a mathematical model to generalize the classical approach of compound interest and to overcome the time structure problem of the interest rates. We introduce a suitable stochastic process called the ‘gauge’ process such that its product with the value of any security is assumed to be a martingale in an appropriate probability space. The framework of this model gives a stochastic actualization formula for the pricing of general securities with options and includes Black and Schole's formula without using arbitrage arguments. Emphasis has been placed on numerical calculation.     

Option pricing under joint dynamics of interest rates, dividends, and stock prices

This paper proposes a unified framework for option pricing, which integrates the stochastic dynamics of interest rates, dividends, and stock prices under the transversality condition. Using the Vasicek model for the spot rate dynamics, I compare the framework with two existing option pricing models. The main implication is that the stochastic spot rate affects options not only directly but also via an endogenously determined dividend yield and return volatility; consequently, call prices can be decreasing with respect to interest rates.     

Asymptotic approach to the pricing of geometric asian options under the CEV model

This paper studies the pricing of Asian options whose payoffs depend on the average value of an underlying asset during the period to a maturity. Since the Asian option is not so sensitive to the value of underlying asset, the possibility of manipulation is relatively small than the other options such as European vanilla and barrier options. We derive the pricing formula of geometric Asian options under the constant elasticity of variance (CEV) model that is one of local volatility models, and investigate the implication of the CEV model for geometric Asian options.     

随机利率下奇异期权的定价公式

在随机利率条件下,借助于测度变换获得了复合看涨期权的一般的定价公式,同时利用鞅理论和Girsanov定理,在利率服从于扩展的Vasicek利率模型时,得到了复合看涨期权精确的定价公式.用同样的方法,考虑了预设日期的重置看涨期权的定价问题,在利率服从同样的利率模型时,获得了重置看涨期权的定价公式.数值化的结果进一步说明了当利率遵循扩展的Vasicek利率模型时,B-S看涨期权的价格关于标的资产的价格是严格单调递增的,复合看涨期权的Geske公式是可以推广到随机利率的情况.     

分数布朗运动下几何平均亚式权证的定价

假设股票价格变化过程服从几何分数布朗运动,建立了分数布朗运动下的亚式期权定价模型.利用分数-It-公式,推导出分数布朗运动下亚式期权的价值所满足的含有三个变量偏微分方程.然后,引进适当的组合变量,将其定解问题转化为一个与路径无关的一维微分方程问题.进一步通过随机偏微分方程方法求解出分数布朗运动下亚式期权的定价公式.最后利用权证定价原理对稀释效用做出调整后,得到分数布朗运动下亚式股本权证定价公式.<正>~~     

双随机跳扩散模型下亚式期权的定价

研究了双随机跳扩散模型下的亚式期权的定价问题.首先引入一个双随机跳扩散过程.然后通过测度变换消除了亚式期权定价中的路经依赖性问题.最后利用鞅定价方法和Ito引理得到了跳扩散模型下的亚式期权价格必须满足的一个积微分方程.通过数值求解该积微分方程就可以得到了亚式期权的价格,供投资者参考.