The Study On Behaviors Of Precautionary Paying For Stochastic Improvements Under Background Risks

Future risks affect people's life, the enterprise's growth and the sustainable development of the society. In order to reduce the impact of future risks, decision-makers must face a trade-off between the sacrifice of current cost and the improvement of future risks, and often undertake precautionary decision-making activities, such as saving, insurance, self-protection. In theoretical study, since 1960s, the study on precautionary saving motivates plenty of the analysis of precautionary decision-making activities. Moreover, the conclusions on both background risk and high-order risk aversion attitudes enrich this kind of study.Within the two-dimensional framework, this work proposes a two-period precautionary decision model which generalizes the two-period saving and self-protection problem. As we know, many risks may appear simultaneously in the real dicision-making setting, so the optimal decision-making needs us to consider the effect of background risk. So as to clarify this effect, this work uses stochastic dominance criterion to characterize the improvement types of the future wealth distribution under the increase of mariginal paying and judge the "good" and "bad" of different risks, and shows the effect of high-order risk aversion attitudes on the optimal precautionary paying level.In order to clarify the joint effect of both background risk and high-order risk aversion attitudes on on the optimal precautionary paying. We also examine the relationships between higher-order risk aversion attitudes. Although many researchers use these concepts separately to examine the economics under risks and think these aspects of risk preferences are independent, other researchers think these concepts are not independent. It seems that a divergence arises. This work shows that prudence may imply risk loving; certainly, prudence also may imply risk aversion. Thus, risk prudence may be a more generalized concept than risk aversion. Moreover, we find the s-shape utility function may be more suitable for one prudent decision-maker.When exploring the precautionary paying, this work links the theory of "risk appointment" to the monotone comparative statics literature and overcomes the difficulties caused by the non-concavity of the model. We show for the corss-prudent decision-maker, the introduction of one independent background risk in the first period will reduce optimal precautionary paying, but the introduction of one independent background risk in the second period will increase optimal precautionary paying. When background risk is introduced in the second period and the increase of mariginal paying improves the future wealth distribution in the sense of high-order stochastic dominance, we find that the impact of deteriorations of one independent background risk on the precautionary paying is consistent to signing cross derivatives of bivariate utility functions. We also use these conclusions to analyze the precautionary saving, precautionary effort and managerial motivation etc.. In doing so, we examine the change of different precautionary behaviors for the decision-makers who can be risk seeking, risk averse or risk seeking in some intervals, but risk averse in others and for the future risk which may obey a general risk distribution.In short, in the decision-making under uncertainties, we need deeply analyze the behaviors of precautionary paying. So, this work tries to understand how the introduction and deteriorations of background risks affect the decision-maker's current willingness to pay for a stochastic improvement of the future risk. Especially, this work avoids some assumption assuring the concavity of model, such as, we don't need assume that the decision-maker is risk aversion or loss probability is concave in the effort level. As a result, we extend the conclusions of previous works on saving, self-protection and managerial motivation etc..