The Partial Order Relation Of Risk And The Nature Of Risk

The relations between the partial order or dependent measure, the expected utility or distorted expection and equality in distribution are considered by this paper. The partial order is divided into two, one is weaker than the supermodular order; another is stronger than the supermodular order. Dependent measures mainly consider two di?erent measures of dependence, one is distribution function; another is tail distribution function.In this paper, we show that under what circumstances the two kinds of risk in di?erent business are the same. One is the partial order by comparing the two risks; another is the dependent measures of the two kinds of risk. In this paper, we focus on conditions about what the two n-dimensional risks is the same. We de?ne three kinds of partial order and two kinds of measure of dependence. One of the partial order is concordance order which is a weaker partial order. One of the partial order is correlation order which is de?ned based on the covariance. One of the partial order is weak conditional increasing order de?ned by the factors of in?uencing the risk. The two dependent measures are the distribution function and tail distribution function of random vectors. And they demand the risks in the same space or in the same business of an insurance company. At the end, we get the conditions about what the two kinds of risk are the same and the change of the ruin probability under partial orders.According to contents, the thesis is divided into four sections. In Chapter one, we introduce the background, present situation and signi?cance of the study. In Chapter two,we mainly introduce several partial orders and the de?nition of the expected utility and distorted expection, then prove the relation between these partial orders and equality in distribution. In Chapter three, we introduce two di?erent measures of dependence then prove the relation between the two di?erent measures of dependence, the expected utility or distorted expection and equality in distribution. In Chapter four, we research the change of the ruin probability under partial orders.