由Lvy过程驱动的BSDE定义的一般非线性期望

本文研究了平凡可积随机变量的一类非线性期望f-期望.利用陈增敬推广g-期望的方法,扩张了f-期望的定义空间.     

Lévy过程驱动的BSDE的反比较定理与Jensen不等式（英文）

本文研究了由一维Lévy过程驱动的倒向随机微分方程(BSDE)的反比较定理.利用一般g-期望下BSDE的反比较定理的证明方法,推导出了一般f-期望下BSDE的反比较定理,并给出了一般f-期望下Jensen不等式成立的充分必要条件.     

关于扭曲数学期望的几个性质

本文研究了扭曲数学期望. 利用构造示性函数的方法, 证明了扭曲数学期望满足常数平移不变性的充要条件是该扭曲数学期望是熵期望.     

关于扭曲数学期望的几个性质

本文研究了扭曲数学期望.利用构造示性函数的方法,证明了扭曲数学期望满足常数平移不变性的充要条件是该扭曲数学期望是熵期望.     

一类f鞅的极大值不等式(英文)

本文研究了f框架下有关f-鞅的不等式性质.利用构造停时的方法和带跳的倒向随机微分方程的比较定理,得到了一类f-鞅的极大值不等式,推广了经典鞅论中的极大值不等式.     

一般的非线性数学期望—g—期望

彭实戈利用倒向随机微分方程引入了平方可积随机变量的非线性数学期望－ｇ－期望,本文扩张了ｇ－期望的定义空间。     

L~p空间中随机变量的g-期望与条件g-期望

利用倒向随机微分方程的Lp解定义了Lp空间中随机变量g-期望与条件g-期望,扩张了g-期望与条件g-期望的定义空间;证明了用Lp解定义的g-期望与文[5]用算子连续扩张方法定义的一般g-期望的一致性,得到了Lp空间中随机变量的g-期望与条件g-期望的一些性质.     

Lp空间中随机变量的g-期望与条件g-期望

利用倒向随机微分方程的Lp解定义了Lp空间中随机变量g-期望与条件g-期望,扩张了g-期望与条件g-期望的定义空间;证明了用Lp解定义的g-期望与文[5]用算子连续扩张方法定义的一般g-期望的一致性,得到了Lp空间中随机变量的g-期望与条件g-期望的一些性质.     

Choquet期望,最大(最小)期望和推广的Peng’s g-期望（英文）

Choquet期望和最大(最小)期望是非线性期望,它们替代经典的数学期望被广泛地应用在经济、金融和保险中.但是,由于非线性,计算它们往往非常困难.本文首先介绍推广的Peng’s g-期望及其相关性质;然后,给出最大(最小)期望和推广的Peng’s g-期望之间的关系;最后,利用Peng’s g-期望,在一些合理假设下,得到Choquet期望和最大(最小)期望是一致的.     

一个离散型随机变量数学期望的几种简捷求法

直接利用期望定义来求离散型随机变量的数学期望,有时计算比较困难.利用条件数学期望、随机变量的和式分解、对称性,分别给出了一个离散型随机变量数学期望的几种求法.     

Jensen’s Inequality Under Nonlinear Expectation Generated by BSDE with Jumps

Acta Mathematicae Applicatae Sinica, English Series - In this paper, we study Jensen’s inequality under f-expectation, which is a nonlinear expectation generated by backward stochastic...     

Nonlinear elliptic differential equations with multivalued nonlinearities

In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all ℝ. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of ℝ. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).     

信用传染违约Aalen加性风险模型

本文考虑了基于加性风险模型的信用风险违约预报模型,不但考虑了宏观因素和公司个体因素,并且通过引入行业因素来刻画公司间可能存在的不同于宏观因素的信用传染效应,由此克服了以往模型对违约相关性的低估.本文在参数加性风险模型下给出极大似然估计及渐近性,提出两种估计方法并比较二者表现,得到最优权估计更加有效.同时本文还考虑了半参数的风险模型,并基于鞅的估计方程得到其估计及渐近性,均得到不错的结果.     

Estimation of error variance in ANOVA model and order restricted scale parameters

We consider the estimation of error variance in the analysis of experiments using two level orthogonal arrays. We address the estimator which is the minimum of all the estimators which we obtain by pooling some sums of squares for factorial effects. Under squared error loss, we discuss whether or not this estimator uniformly improves upon the best positive multiple of error sum of squares. We show that when we have two factorial effects, we obtain uniform improvement. However, we show that when we have more than two factorial effects, we cannot necessarily obtain uniform improvement. Further, the above results are applied to the problem of estimating the smallest scale parameter of chi-square distributions.     

Exploring an unknown graph

We wish to explore all edges of an unknown directed, strongly connected graph. At each point, we have a map of all nodes and edges we have visited, we can recognize these nodes and edges if we see them again, and we know how many unexplored edges emanate from each node we have visited, but we cannot tell where each leads until we traverse it. We wish to minimize the ratio of the total number of edges traversed divided by the optimum number of traversals, had we known the graph. For Eulerian graphs, this ratio cannot be better than two, and two is achievable by a simple algorithm. In contrast, the ratio is unbounded when the deficiency of the graph (the number of edges that have to be added to make it Eulerian) is unbounded. Our main result is an algorithm that achieves a bounded ratio when the deficiency is bounded. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 265–297, 1999     

Optimal control of nonlinear evolution inclusions

In this paper, we study the optimal control of nonlinear evolution inclusions. First, we prove the existence of admissible trajectories and then we show that the set that they form is relatively sequentially compact and in certain cases sequentially compact in an appropriate function space. Then, with the help of a convexity hypothesis and using Cesari's approach, we solve a general Lagrange optimal control problem. After that, we drop the convexity hypothesis and pass to the relaxed system, for which we prove the existence of optimal controls, we show that it has a value equal to that of the original one, and also we prove that the original trajectories are dense in an appropriate topology to the relaxed ones. Finally, we present an example of a nonlinear parabolic optimal control that illustrates the applicability of our results.This research was supported by NSF Grant No. DMS-88-02688.     

The value of foresight

Suppose you have one unit of stock, currently worth 1, which you must sell before time $T$. The Optional Sampling Theorem tells us that whatever stopping time we choose to sell, the expected discounted value we get when we sell will be 1. Suppose however that we are able to see $a$ units of time into the future, and base our stopping rule on that; we should be able to do better than expected value 1. But how much better can we do? And how would we exploit the additional information? The optimal solution to this problem will never be found, but in this paper we establish remarkably close bounds on the value of the problem, and we derive a fairly simple exercise rule that manages to extract most of the value of foresight.     

Some non-interior path-following methods based on a scaled central path for linear complementarity problems

In this paper we present some non-interior path-following methods for linear complementarity problems. Instead of using the standard central path we use a scaled central path. Based on this new central path, we first give a feasible non-interior path-following method for linear complementarity problems. And then we extend it to an infeasible method. After proving the boundedness of the neighborhood, we prove the convergence of our method. Another point we should present is that we prove the local quadratic convergence of feasible method without the assumption of strict complementarity at the solution.     

Asymptotic behaviour of a closed‐loop thermosyphon with linear friction and viscoelastic binary fluid

Viscoelastic fluids represent a major challenge both from an engineering and from a mathematical point of view. Recently, we have shown that viscoelasticity induces chaos in closed‐loop thermosyphons even when we consider binary fluids, this is, when we consider a solute in the fluid, as water and antifreezes, for example. In this work, we consider a linear friction law, and we show that in this case with the addition of a solute to the fluid we can prove, under some conditions, chaotic asymptotic behavior for suitable geometry of the circuit and heat flux or ambient temperature functions.