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	1. Two sufficient conditions for convex ordering on risk aggregation
	Zhu Dan,Yin Chuancun
	Mathematics 22 April 2017
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	Abstract:In this paper, we define new stochastic orders in higher dimensions called weak correlation orders. It is shown that weak correlation orders imply stop-loss order of sums of multivariate dependent risks with same marginals. Moreover, some properties and relations of stochastic orders are discussed.
	TO cite this article:Zhu Dan,Yin Chuancun. Two sufficient conditions for convex ordering on risk aggregation[OL].[22 April 2017] http://en.paper.edu.cn/en_releasepaper/content/4725444


	2. On the comparison theorem for $1$-dimensional generalized anticipated BSDEs
	XU Xiao-Ming
	Mathematics 19 November 2014
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	Abstract:In this paper, we will establish a general comparison theoremfor the following $1$-dimensional generalized anticipated backward stochastic differential equation(GABSDE):egin{equation}left{egin{tabular}{rlll}$-dY_t$ &=& $f(t, {Y_r}_{rin [t, T+C]}, {Z_r}_{rin [t,T+C]})dt-Z_tdB_t, $ & $tin[0, T];$\$Y_t$ &=& $xi_t, $ & $tin[T, T+C];$\$Z_t$ &=& $eta_t, $ & $tin[T, T+C].$end{tabular} ight.end{equation}
	TO cite this article:XU Xiao-Ming. On the comparison theorem for $1$-dimensional generalized anticipated BSDEs[OL].[19 November 2014] http://en.paper.edu.cn/en_releasepaper/content/4619509

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	3. Probabilistic representation for solution of some coupled system of quasilinear parabolic PDEs
	XU Xiao-Ming
	Mathematics 11 November 2014
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	Abstract:In this paper, we obtain a probabilistic representation for thesolution of the following coupled system of quasilinear parabolicPDEs:egin{equation}left{egin{tabular}{ll}$partial_t u^0+ b u_x^0+rac{1}{2}sigma^2 u_{xx}^0+(Deltau-delta u_x^0)gamma_t+f(t, x, u^0, u_x^0 sigma, Delta u)=0,$\$partial_t u^1+ b u_x^1+rac{1}{2}sigma^2 u_{xx}^1+f(t, x, u^1,u_x^1sigma, Delta u)=0,$\$u^0(T, x)=arphi(0, x)in mathbb{R},$\$u^1(T,x)=arphi(1, x)in mathbb{R},$end{tabular} ight.end{equation}where $Delta u(t, x)=u^1(t, x+delta(t, x))-u^0(t, x)$ and $b$,$sigma$, $delta$ are $mathbb{R}$-valued functions defined on $[0,T] imes mathbb{R}$, by introducing a new kind of backwardstochastic differential equation, called BSDE with random defaulttime.
	TO cite this article:XU Xiao-Ming. Probabilistic representation for solution of some coupled system of quasilinear parabolic PDEs[OL].[11 November 2014] http://en.paper.edu.cn/en_releasepaper/content/4618172


	4. Precise large deviations for sums of two-dimensional random vectors with dependent components with extended regularly varying tails
	TIAN Hai-Lan,SHEN Xin-Mei
	Mathematics 02 July 2013
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	Abstract:Let ${ec{X}_{k}, k geq 1}$ be a sequence ofindependent identically distributed non-negative random vectors withcommon marginal distributions $F_{1}$, $F_{2}$ having extendedregularly varying tails, joint distribution function $F_{1,2}$ andfinite mean $ec{mu}=epec{X}_{1}$. The two components of$ec{X}_{1}$ are allowed to be dependent. Under some mildassumptions, precise large deviations for both the partial sums$ec{S}_{n}=sum_{k=1}^{n}ec{X}_{k}$ and the random sums$ec{S}_{N(t)}=sum_{k=1}^{N(t)}ec{X}_{k}$ are investigated,where $N(t)$ is a counting process independent of the sequence${ec{X}_{k}, k geq 1}$.
	TO cite this article:TIAN Hai-Lan,SHEN Xin-Mei. Precise large deviations for sums of two-dimensional random vectors with dependent components with extended regularly varying tails[OL].[ 2 July 2013] http://en.paper.edu.cn/en_releasepaper/content/4549936


	5. Bilateral Counterparty Risk Valuation for CDS in a Contagion Model Using Markov Chain
	Dong Yinghui,Wang Guojing
	Mathematics 09 December 2012
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	Abstract:The computation of the bilateralcounterparty valuation adjustment of CDS is in effect the modelingof the default correlation between the investor, the protectionseller, and the reference entity. We present a contagion model,where defaults of three parties are all driven by a commoncontinuous-time Markov process. We give the explicit formula for thebilateral credit valuation adjustment (CVA) of the CDS and examinethe effect of the regime switching on the CVA.
	TO cite this article:Dong Yinghui,Wang Guojing. Bilateral Counterparty Risk Valuation for CDS in a Contagion Model Using Markov Chain[OL].[ 9 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4502104


	6. Phase Changes in the Topological Indices of Scale-free Trees
	FENG Qunqiang,HU Zhishui
	Mathematics 18 January 2012
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	Abstract:A scale-free tree with the parameter β is very close to a star if βis just a bit larger than -1, whereas it is close to a randomrecursive tree if β is very large. Through the Zagreb index, the whole scene of the evolution of the scale-free trees model is consideredas β goes from -1 to +∞. And the first two moments and the asymptotic behaviors of this index of a scale-free tree are obtained for all β>-1.
	TO cite this article:FENG Qunqiang,HU Zhishui. Phase Changes in the Topological Indices of Scale-free Trees[OL].[18 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4462894


	7. The Hitting Time for a Cox Risk Process
	Wu Rong ,Wang Wei
	Mathematics 18 January 2012
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	Abstract:This paper investigates the hitting timeand the last exit time of a Cox risk process whose intensity processis a markovian jump process. By a ``backward differential argument"and the Markov property of the intensity process, we derive theintegro-differential equation satisfied by the Laplace transform ofthe hitting time. Exact solution to this equation could beconstructed by the probability method. Further, we investigate thesituation when the intensity process is an n-state Markov process
	TO cite this article:Wu Rong ,Wang Wei . The Hitting Time for a Cox Risk Process[OL].[18 January 2012] http://en.paper.edu.cn/en_releasepaper/content/4457932


	8. Gradient flows on Wasserstein space over abstract Wiener space
	Shao Jinghai ,Karl-Theodor STURM
	Mathematics 13 February 2009
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	Abstract:The properties of the space of all probability measures on the abstract Wiener space are studied. The relation between absolutely continuous curves and continuity equations is completed characterized, and the derivatives of Wasserstein distance along these curves are given. We extend Ambrosio-Gigli-Savare\\\
	TO cite this article:Shao Jinghai ,Karl-Theodor STURM. Gradient flows on Wasserstein space over abstract Wiener space[OL].[13 February 2009] http://en.paper.edu.cn/en_releasepaper/content/28985


	9. Modified logarithmic Sobolev inequalities and transportation cost inequalities in $\\\\\\\\mathbb{R}^n$
	Shao Jinghai
	Mathematics 13 February 2009
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	Abstract:In this paper, the modified logarithmic Sobolev inequalities and transportation cost inequalities for measures with density $e^{-V}$ in $\\\\\\\\R^n$ are established. It is proved by using Pr\\\\\\\\\\\\\\\
	TO cite this article:Shao Jinghai . Modified logarithmic Sobolev inequalities and transportation cost inequalities in $\\\\\\\\mathbb{R}^n$[OL].[13 February 2009] http://en.paper.edu.cn/en_releasepaper/content/28947


	10. Explicit Expressions for the Comparison Theorems of Multidimensional BSDEs
	xu yuhong
	Mathematics 23 May 2008
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	Abstract:In this Note, we give explicit expressions for the comparison theorem of multidimensional backward stochastic differential equations (BSDEs in short) and for the viability property on a rectangle.
	TO cite this article:xu yuhong. Explicit Expressions for the Comparison Theorems of Multidimensional BSDEs[OL].[23 May 2008] http://en.paper.edu.cn/en_releasepaper/content/21685

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