G-expectation And Inequality For G-expectation

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.