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Approximate solutions to infinite dimensional LQ problems over infinite time horizon

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Science china mathematics 2006年第7期49卷 865-876页

作者： PAN Liping, ZHANG Xu & CHEN Qihong School of Mathematical Sciences, Fudan university, shanghai 200433, china School of mathematics, Sichuan university, Chengdu 610064, china department of applied mathematics, shanghai university of finance & economics, shanghai 200433, china School of Mathematical Sciences Fudan University Shanghai China School of mathematics Sichuan University Chengdu China department of applied mathematics Shanghai University of Finance & Economics Shanghai China

This paper is addressed to develop an approximate method to solve a class of infinite dimensional LQ optimal regulator problems over infinite time horizon. Our algorithm is based on a construction of approximate solutions which solve some finite dimensional LQ optimal regulator problems over finite time horizon, and it is shown that these approximate solutions converge strongly to the desired solution in the double limit sense.

关键词： approximate solution, LQ problem, infinite dimensional, infinite time horizon.

Global Well-Posedness of the BCL System with Viscosity

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Chinese Annals of mathematics,Series B 2009年第2期30卷 153-172页

作者： Junqi HU department of applied mathematics Shanghai University of Finance and Economics Shanghai 200433 China

The BCL system, a kind of equations governing the motion of the free surface of water waves in R3, is studied. Some results on the global existence, uniqueness and regularity of solutions to such system with small ini... 详细信息

关键词： L系统适定性粘度运动方程原始数据水面波

Construct non-graded bi-Frobenius algebras via quivers

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Science china mathematics 2007年第3期50卷 450-456页

作者： Yan-hua WANG & Xiao-wu CHEN department of applied mathematics, shanghai university of finance and economics, shanghai 200433, china department of mathematics, university of Science and Technology of china, Hefei 230026, china department of applied mathematics Shanghai University of Finance and Economics Shanghai China department of mathematics University of Science and Technology of China Hefei China

Using the quiver technique we construct a class of non-graded bi-Frobenius algebras. We also classify a class of graded bi-Frobenius algebras via certain equations of structure coefficients.

关键词： quivers bi-Frobenius algebras graded algebras.

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双币种永久美式期权定价

内蒙古大学学报（自然科学版） 2013年第3期44卷 261-265页

作者：郭培栋陈启宏上海工程技术大学管理学院上海201620 上海财经大学应用数学系上海200433

在Black-Scholes框架下,利用无套利定价方法,建立了双币种永久美式期权的定价模型,并分析了敲定价分别以国内货币计价和国外货币计价下的双币种永久美式期权的定价问题,通过运用偏微分方程的方法得到了这两种情形下期权价格的显式解.最... 详细信息

在Black-Scholes框架下,利用无套利定价方法,建立了双币种永久美式期权的定价模型,并分析了敲定价分别以国内货币计价和国外货币计价下的双币种永久美式期权的定价问题,通过运用偏微分方程的方法得到了这两种情形下期权价格的显式解.最后通过数值模拟,分析了标的资产和汇率的波动水平以及相关系数对期权的最优执行策略和期权价格的影响.

关键词：双币种期权永久美式期权期权定价定价模型

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一类椭圆方程很弱解关于区域的连续性

数学年刊（A辑） 2001年第6期22卷 783-790页

作者：冉启康方爱农上海财经大学应用数学系上海200433 上海交通大学应用数学系上海200030

本文讨论了二阶椭圆型方程－Δｕ＝ｆ（ｘ，ｕ），ｘ∈Ω的Ｄｉｒｉｃｈｌｅｔ问题ｕ｜Ω＝０的很弱解ｕ∈Ｗ０１，ｒ（Ω）（１＜ｒ＜２）关于区域Ω的连续性及很弱边值问题的很弱解的唯一性．

关键词：很弱解 Hodge分解很弱边值问题二阶椭圆型方程 Dirichlet问题连续性

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弧连通函数的最优性条件

铜仁学院学报 2008年第2期2卷 97-104页

作者：雷晓军梁治安铜仁学院数学系上海财经大学应用数学系贵州铜仁554300 上海220043

文章在弧连通集S■Rn上的实值函数f:S→R是弧连通函数的定义下,给出相关的广义弧连通函数定义。这类函数是凸性的推广,它们满足确定的局部-全局极值性。反过来,在某些条件下,满足局部-全局极值性的函数必是这些广义函数类之一。在广义... 详细信息

文章在弧连通集S■Rn上的实值函数f:S→R是弧连通函数的定义下,给出相关的广义弧连通函数定义。这类函数是凸性的推广,它们满足确定的局部-全局极值性。反过来,在某些条件下,满足局部-全局极值性的函数必是这些广义函数类之一。在广义弧连通的假设下建立了约束规划(ACP)min x∈Sf(x),s.t.g(x)≤0的最优性充分条件。

关键词：弧连通函数广义凸性局部—全局极值性最优性条件

Stability of Solution of a Class of Quasilinear Elliptic Equations

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Acta Mathematicae Applicatae Sinica 2002年第3期18卷 461-470页

作者： Qi-kang Ran, Ai-nong Fangdepartment of applied mathematics, shanghai university of finance and economics, shanghai 200433, chinadepartment of applied mathematics, shanghai Jiaotong university, shanghai 200030, china department of applied mathematics Shanghai University of Finance and Economics Shanghai China department of applied mathematics Shanghai Jiaotong University Shanghai China

In this paper, using capacity theory and extension theorem of Lipschitz functions we first discuss the uniqueness of weak solution of nonhomogeneous quasilinear elliptic equationsin space W(θ,p)(Ω), which is bigger than W1,p(Ω). Next, using revise reverse Holder inequality we prove that if ωc is uniformly p-think, then there exists a neighborhood U of p, such that for all t ∈U, the weak solutions of equation corresponding t are bounded uniformly. Finally, we get the stability of weak solutions on exponent p.

关键词： Nonhoraogeneous quasilinear elliptic equations capacity stability

A Note on Twisted Hopf Algebras

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Journal of Mathematical Research with Applications 2012年第5期32卷 582-588页

作者： Yanhua WANG department of applied mathematics,shanghai university of finance and economics,shanghai 200433,P.R.china department of applied mathematics Shanghai University of Finance and Economics Shanghai 200433

In this paper,we get some properties of the antipode of a twisted Hopf *** proved that the graded global dimension of a twisted Hopf algebra coincides with the graded projective dimension of its trivial module k,which... 详细信息

关键词： Hopf algebras twisted Hopf algebras projective dimension global dimension.

Saddlepoint approximations for studentized compound Poisson sums with no moment conditions in audit sampling

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Science china mathematics 2010年第12期53卷 3131-3138页

作者： ZHOU GuoLiang 1 & ZHOU Wang 2, 1 Institute of Accounting and finance, shanghai university of finance and economics, shanghai 200433, china 2 department of Statistics and applied Probability, National university of Singapore, Singapore 117546, Singapore Institute of Accounting and finance Shanghai University of Finance and Economics Shanghai China department of Statistics and applied Probability National University of Singapore Singapore Singapore

Saddlepoint approximations for the studentized compound Poisson sums with no moment conditions in audit sampling are derived. This result not only provides a very accurate approximation for studentized compound Poisson sums, but also can be applied much more widely in statistical inference of the error amount in an audit population of accounts to check the validity of financial statements of a firm. Some numerical illustrations and comparison with the normal approximation method are presented.

关键词： saddlepoint approximation Laplace approximation self-normalized compound Poisson sum stu- dentized compound Poisson sum