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	1. Markov skeleton process in PERT networks
	Xiangxing Kong,Xuan Zhang,Zhenting Hou
	Mathematics 13 January 2009
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	Abstract:In this paper we investigate Programming Evaluation and Review Technique networks with independently and generally distributed activity durations. For any path in this network, we select all the activities related to this path such that the completion time of the sub-network (only consist of all the related activities) is equal to the completion time of this path. We use the elapsed times as the supplementary variables and model this sub-network as a Markov Skeleton Process, the state space is related to the sub-network structure. Then use the backward equation to compute the distribution of the sub-network\
	TO cite this article:Xiangxing Kong,Xuan Zhang,Zhenting Hou. Markov skeleton process in PERT networks [OL].[13 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27699


	2. Necessary and Sufficient Conditions for Positive and Negative Solutions of BSDEs with Continuous Coefficients
	XU Yuhong
	Mathematics 08 December 2008
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	Abstract:As we know that, in stochastic finance, each pricing mechanism corresponds to a well-defined BSDE. The behaviors of g exert an influence to this mechanism. In some circumstances, to regulate or to design a pricing mechanism is in fact to find a suitable generating function g. By a technical result on the local limit of solutions to backward stochastic differential equations (BSDEs for short), this note gives necessary and sufficient conditions on g for positive and negative solutions of BSDEs with continuous coefficients, which implies that there is no arbitrage to the pricing mechanism characterized by these BSDEs.
	TO cite this article:XU Yuhong. Necessary and Sufficient Conditions for Positive and Negative Solutions of BSDEs with Continuous Coefficients[OL].[ 8 December 2008] http://en.paper.edu.cn/en_releasepaper/content/26372

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	3. On the Comparison and Uniqueness for Solutions of BSDEs with　Continuous Coefficients
	Yuhong Xu
	Mathematics 05 November 2008
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	Abstract:As we known that there may be more than one solution for backward stochastic differential equation with continuous coefficients and the comparison theorem for any solutions of two BSDEs does not hold in general in this setting. In fact, there is a close relation between the uniqueness and the comparison for solutions of BSDEs. This note proves that, for one dimensional BSDEs with continuous coefficients, there is a unique solution if and only if the comparison for any solutions of two BSDEs holds true.
	TO cite this article:Yuhong Xu. On the Comparison and Uniqueness for Solutions of BSDEs with　Continuous Coefficients　[OL].[ 5 November 2008] http://en.paper.edu.cn/en_releasepaper/content/25428


	4. Multidimensional g-expectations and Risk Measures
	xu yuhong
	Mathematics 02 October 2008
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	Abstract:This paper proposes a notion of multidimensional g-expectations which provide a multidimensional version of nonlinear expectations. By a technical result on explicit expressions for the comparison theorem of multidimensional backward stochastic differential equations, necessary and sufficient conditions are given for the constancy, monotonicity and positivity properties of multidimensional g-expectations; we also prove that a multidimensional risk measure introduced by multidimensional g-expectation is concave if and only if the generator g satisfies a concave-like condition.
	TO cite this article:xu yuhong. Multidimensional g-expectations and Risk Measures[OL].[ 2 October 2008] http://en.paper.edu.cn/en_releasepaper/content/24507


	5. A General Test Theorem for Generators of BSDEs with Continuous Coefficients and Applications
	Xu Yuhong
	Mathematics 19 September 2008
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	Abstract:Test theorems for lipschitz continuous generators of backward stochastic differential equations (BSDEs in short) can be used to test the generating mechanism g of BSDE theoretically. This paper generalizes the test theorem to the case where the coefficient is only continuous; As applications, a converse comparison theorem for generators of BSDEs is obtained; we also give necessary and sufficient conditions for positive and negative solutions of BSDEs.
	TO cite this article:Xu Yuhong. A General Test Theorem for Generators of BSDEs with Continuous Coefficients and Applications[OL].[19 September 2008] http://en.paper.edu.cn/en_releasepaper/content/24176


	6. Dynamic Programming Principle for One Kind of Stochastic Recursive Optimal Control Problem and Hamilton-Jacobi-Bellman Equation
	Wu Zhen,Yu Zhiyong
	Mathematics 30 July 2008
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	Abstract:In this paper, we study one kind of stochastic recursive optimal control problem with the obstacle constraint for the cost functional described by the solution of a reflected backward stochastic differential equation. We give the dynamic programming principle for this kind of optimal control problem and show that the value function is the unique viscosity solution of the obstacle problem for the corresponding Hamilton-Jacobi-Bellman equation.
	TO cite this article:Wu Zhen,Yu Zhiyong. Dynamic Programming Principle for One Kind of Stochastic Recursive Optimal Control Problem and Hamilton-Jacobi-Bellman Equation[OL].[30 July 2008] http://en.paper.edu.cn/en_releasepaper/content/23153


	7. Viability for One Dimensional BSDEs
	xu yuhong
	Mathematics 23 May 2008
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	Abstract:In this Note, based on the limit theorem between generators and solutions of backward stochastic differential equations (BSDEs in short), we give explicit expressions for the necessary and sufficient conditions of viability property for one dimensional BSDEs under mild assumptions.
	TO cite this article:xu yuhong . Viability for One Dimensional BSDEs[OL].[23 May 2008] http://en.paper.edu.cn/en_releasepaper/content/21691


	8. 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


	9. Comparison and Control Theorems for the Second Part of Solutions to BSDEs
	xu yuhong
	Mathematics 20 May 2008
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	Abstract:This note explores properties of the second part of solutions (Y,Z) to backward stochastic differential equations via Malliavin calculus. A comparison theorem and a control theorem are established for Z; we also give sufficient conditions under which Z is a continuous semimartingale.
	TO cite this article:xu yuhong. Comparison and Control Theorems for the Second Part of Solutions to BSDEs[OL].[20 May 2008] http://en.paper.edu.cn/en_releasepaper/content/21569


	10. Test Theorem for Generators of Backward SDEs
	xuyuhong
	Mathematics 05 May 2008
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	Abstract:This Note gives a test theorem for generators of backward stochastic differential equations with continuous coefficients; for an application,we obtain a converse comparison theorem for generators of BSDEs.
	TO cite this article:xuyuhong. Test Theorem for Generators of Backward SDEs[OL].[ 5 May 2008] http://en.paper.edu.cn/en_releasepaper/content/21112

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