The LeChatelier principle for changes in risk

In this paper, we analyze the comparative statics of changes in risk in the context of problems with multiple decision variables. We demonstrate, in particular, that the Samuelson-LeChatelier principle extends naturally to the comparative statics of changes in risk: in the presence of positive feedbacks between the decision variables, the unrestricted response to an increase in risk is in the same direction and stronger in magnitude than the restricted response (i.e. the choice when other decision variables are fixed). We define the concepts of Nth-degree risk complements and Nth-degree risk substitutes and we show that it is in any one of these two cases (and only in these cases) that we will observe positive feedbacks between the decision variables. We also analyze the extent to which the same principle can be applied to strategic settings under uncertainty.