Some Relationships and Properties among the Subsets of Rothschild-Stiglitz Increases in Risk
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This paper explores some interesting relationships and properties among the subsets of Rothschild-Stiglitz (R-S) increases in risk. First, the relatively strong increase in risk (RSIR) shift implies the extended strong increase in risk (ESIR) one which, in turn, implies the left-side extended strong increase in risk (L-ESIR) one. Second, the left-side relatively strong increase in risk (L-RSIR) order lies between the RSIR and the L-ESIR one. In addition, we investigate that the ESIR shift can be decomposed into a series of RSIR shifts. It implies that the comparative statics result made for the set of RSIR shifts can be generalized to the set of ESIR shifts. In other words, given two cumulative distribution function (CDF) orders, an arbitrary change in CDF generated by one CDF order can always be decomposed into a series of shifts that satisfy the other CDF order. Then, if the latter order gives a sufficient condition for a general comparative static result, then all shifts that satisfy the former order are also admissible for the result. Therefore, examining the presence of this kind of relationship between CDF orders is meaningful for making a general comparative static statement.
Abstract
This paper explores some interesting relationships and properties among the subsets of Rothschild-Stiglitz (R-S) increases in risk. First, the relatively strong increase in risk (RSIR) shift implies the extended strong increase in risk (ESIR) one which, in turn, implies the left-side extended strong increase in risk (L-ESIR) one. Second, the left-side relatively strong increase in risk (L-RSIR) order lies between the RSIR and the L-ESIR one. In addition, we investigate that the ESIR shift can be decomposed into a series of RSIR shifts. It implies that the comparative statics result made for the set of RSIR shifts can be generalized to the set of ESIR shifts. In other words, given two cumulative distribution function (CDF) orders, an arbitrary change in CDF generated by one CDF order can always be decomposed into a series of shifts that satisfy the other CDF order. Then, if the latter order gives a sufficient condition for a general comparative static result, then all shifts that satisfy the former order are also admissible for the result. Therefore, examining the presence of this kind of relationship between CDF orders is meaningful for making a general comparative static statement.
참고문헌 (12)
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