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Monotone strong increases in risk and their comparative statics
Author(s) -
Ryu Suyeol,
Yoon SeongMin
Publication year - 2011
Publication title -
international journal of economic theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.351
H-Index - 11
eISSN - 1742-7363
pISSN - 1742-7355
DOI - 10.1111/j.1742-7363.2011.00163.x
Subject(s) - stochastic dominance , comparative statics , stochastic game , monotonic function , cumulative distribution function , mathematics , mathematical economics , monotone polygon , random variable , economics , risk aversion (psychology) , function (biology) , econometrics , expected utility hypothesis , statistics , probability density function , microeconomics , evolutionary biology , mathematical analysis , geometry , biology
We introduce a new concept of the monotone strong increase in risk (MSIR) order that imposes monotonicity restrictions on the ratio of the two cumulative of cumulative distribution functions as a special case of Rothschild–Stiglitz increases in risk that is the subset of the second‐degree stochastic dominance criterion. We show that the MSIR order implies that the conditional expectation of a random variable under one cumulative distribution function is greater than or equal to that under another cumulative distribution function. Restricting the payoff function to be linear in the random variable and limiting our analysis to risk‐averse decision‐makers who are prudent, we obtain appealing comparative statics results for the MSIR shift. This general conclusion can be applied to prevailing economic models having a linear payoff.