【作者】 杨丽；

【导师】 王向荣；

【作者基本信息】 山东科技大学 ， 应用数学， 2008， 硕士

【摘要】 彭实戈通过倒向随机微分方程(以下简记为BSDE)引入了g-期望与条件g-期望的概念,从而建立了动态非线性数学期望理论的基础,经研究发现,g-期望理论在解决一些经济及金融问题上起到了重要作用,为经济理论的研究提供了强有力的工具。g-期望的出现,也促进了非线性数学期望的发展。经许多学者共同努力,得到了关于g-期望的一些良好的性质。在数学的几乎所有分支中,不等式常常起着重要甚至是关键的作用。g-期望的不等式也将在研究g-期望理论中起到关键性的作用,它将是解决g-期望问题的有力工具。为了能更好应用g-期望理论解决实际问题,本文集中对基于g-期望的不等式进行了研究。本文分为五章。第一章绪论介绍了g-期望的基本知识及其研究近况。第二章在基于g-期望的Jensen不等式成立的情况下,得到了基于g-期望的Jensen不等式的有关结论,并讨论了关于二元函数的基于g-期望的Jensen不等式的充要条件。第三章给出了在生成元g满足一定条件下基于g-期望的H(o|¨)lder不等式及Minkowski不等式的推广。第四章证明了基于g-概率的几个不等式。第五章得到了在非Lipschitz条件下关于BSDE的估值不等式。更多还原

【Abstract】 Peng introduces g-expectation and conditional g-expectation by backward stochastic differential equations(BSDE). Thus the foundation of dynamic no-linear mathematics expectation theories is established. Scientist detected that g-expectation plays a key role in solving economic and financial problem and provides powerful toll for studying economic theories. The emergence of g-expectation promoted the development of no-linear mathematics expectation too. Many scholar got some good property of g-expectation by their studying.In almost all branch of mathematics, inequality usually play a key role. The inequality of g-expectation will play a key role in studying theories of g-expectation. It will be the tool of solving the problem for g-expectation. We will study some inequality of g-expectation in this paper.This dissertation includes five parts. Chapter 1 introduces some basic knowledge and current research condition of g-expectation. In chapter 2, the corollary of Jensen inequality for g-expectation is got. We give a necessary and sufficient condition of Jensen inequality for g-expectation for monotonic functions. In chapter 3 , we expaned the H(o|¨)lder inequality and Minkowski inequality when the generator g satisfies some certainty conditions. In chapter 4, some inequality of g-probability are certificated. In chapter 5, we get the estimate value inequality in non-Lipschitz condition.更多还原