Research On The Related Problems Of Anti - Monotonic Risk

In the ?eld of ?nance and insurance, we often consider how to reduce the risk of risk port?ios. It is easy to think that a risk random variable added with conditions makes the risk of the former random variables decreased. In this paper we mainly use the stop-loss order as the risk measure to discuss this issue.In order to make the risk of random variables is reduced, it is easy to think of adding a trend opposite random variable to the former to make the ?nal property loss to the minimum. We introduce the concept of counter-monotonicity. But what kind of this such a speci?c risk which is counter-monotonic with original random variables, is an arbitrary counter-monotonic risk can be used as a risk reducer? This is our mainly problem to discuss. The thesis is divided into three kinds of situations to explore the properties of risk reducer.In this thesis we introduce the stock, option, insurance as examples, to make the thesis more vivid and easier understood.This thesis mainly consider using stop-loss order as the risk measure to reduce the risk, and is divided into ?ve chapters.Chapter 1 Preference, we show the objective and signi?cance of the thesis.Chapter 2 In this chapter, we introduce the meanings and de?nitions of stochastic order, stop-loss order and risk measure, and the properties of them. In the end, we give the de?nitions and some theorems about comonotonicity and countermonotonicityChapter 3 The ?rst section of the third chapter, we will propose the de?nition of some ?nancial terms. Then we will give a simple su?cient conditions to determine the risk reducer, give the de?nition of H(X), and give the explanation of the additional conditions of course. This thesis listed on stop-loss order some new superposition rule and elimination rule, and gives the stop-loss order established conditions. In the third section of the third chapter, the risk reducer of di?erent factor are described. And we describe the given random variable, and the function relation between the risk reducer and stop-loss order.Chapter 4 We will apply the results into the insurance compensation and ensure compensation market research. The nature of insurance schedule has some satisfactory,which is that the contract of insurance will ensure that the risk bearer and the insurer will both bene?t from it.Chapter 5 A brief summary about the full text is made in the last chapter.