Theoretical Analysis And Applications On Higher-order Risk Aversion Behaviors

Recently, in order to deeply learn and analyze the economic and financial phenomenon in the real world, the analysis on the economic and financial decision-making under uncertainties is focusing on the effect of the risk-taking behaviors. Since1960s, the general risk aversion theory has become a standard theory-choice foundation to deal with the effect of the risk aversion behavior, and it arouses a number of studies on other complex risk-taking behaviors. Especially, the behaviors of higher-order risk aversion (risk prudence, risk temperance etc.) and the effects of background risks receive increasing attentions, since not only, in some degree, they can explain such the equity premium puzzle etc. as the economic and financial anomalies, but also the exploration on these concepts is helpful to make the optimal choice on saving or investment etc..As we know, the introduction of background risks makes the decision-model closer to the real case and confirms the importance of higher-order risk aversion behaviors. This paper uses the definitions of stochastic dominance and risk increase to judge the "good" and "bad" of risks. Basing on these criterions, we can demonstrate that the effect of deteriorations of any background risk depends on the properties of decreasing Ross risk aversion measures. However, similar to previous works in the expected-utility framework, the analysis also uses mathematical expressions to describe the higher risk aversion behavior. Thus, so as to clarify the essence of higher risk aversion behaviors, we generalize the theory-choice foundation which uses the lottery pairs to characterize decision-makers’preference behaviors. Interestingly, basing on the lottery pairs in "additive risk apportionment", we can design multiplicative lottery pairs to measure the strength of higher risk aversion behaviors. Moreover, regardless of one-dimensional case and two-dimensional case, or "additive risk apportionment" and "multiplicative risk apportionment", the essence of the characterization of lottery pairs is that the combination between "good" with "bad" or "bad" with "bad" is beneficial to decision-makers. The former is "hedging" of risks, the later can be seen as the investment strategy "put all eggs in one basket". So, our analysis is helpful to intuitively clarify the essence of higher risk aversion behavior and its effect on the real decision-making.In order to apply our conclusions, this paper explores the effects of higher-order risk aversion behaviors in the real economic and financial decision-making. For the incentive contract with interim, participation constraints, we show the principal with stronger Arrow-Pratt risk aversion degree is ready to allocate more production to the inefficient agent; We take the precautionary saving model as an example to discuss how to apply the characterization of lottery pairs in real decision-making models; We study the joint effect of two risks in the presence of a non-labor income uncertainty and a stochastic wage risk.In a word, the research of the decision-making under uncertainties is focusing on characterizations, measures of complex risk-taking behaviors. The conclusions on higher risk aversion behaviors are also applied in empirical studies and the real decisions. Thus, we further study this kind of problem. It is worth noting that the characterization of lottery pairs is available within non-expected utility models;More importantly, the emphasis of the conclusions is not the mathematical expressions in the relevant results, but the economic implications behind the mathematical symbols and the information they can provided.