Some Studies On Several Types Of Random Order Problems

This thesis mainly researches some stochastic orders and their properties. The stochastic order is an important, instrument for researching managers and investors' choice. which can help us to know the preference of investors better. We can also achieve that the result matches with the factor about investors' choice by the different definitions of stochastic orders. Therefore, a lot of scholars do deeply research about it, and achieve many classic results. The thesis further discusses the properties of stochastic orders based on primary results.The first chapter of this thesis introduces the research backgrounds of stochastic orders.The second chaptcer of this thesis introduces the basic definitions and theorems. such as risk measure, comonotonicity, mutual exclusivity, and several definitions of stochastic orders,properties and relations. A good stochastic order should be able to rcflect the severity of risk, the preference of investors. In addition, it needs the simple formula. The third chapter of this thesis introduces the relation between risk measures and stochastic orders firstly.Secondly, the theorem about correlation is improved by changing the simpler condition,and is proved in the other way. Finally, I introduce a new stochastic order and give some properties about it, especially, the relations between a new stochastic order and others, which is the main result of this paper.