Strongly More Risk Averse Revisited [ 1] July 13, 2012 Liqun Liu Jack Meyer

Strongly More Risk Averse Revisited[1] July 13, 2012 Liqun Liu Jack Meyer Private Enterprise Research Center Department of Economics Texas A&M University Michigan State University College Station, TX 77843 East Lansing, MI 48824 [1] Support from the Private Enterprise Research Center at Texas A&M University is gratefully acknowledged.

. Ross: u(x) is strongly more risk averse than v(x) if and only if i) There exists a  > 0 such that  for all x and y ii) There exists a  > 0 and function (x) with '(x)  0 and ''(x)  0 such that u(x) = ·v(x) + (x) for all x.

The measure of Concave Risk Aversion is defined as C(x) =

Theorem 2: Cu(x) Cv(x) for all x in [a, b] if and only if u(x) is strongly more risk averse than v(x) on [a, b].

Tu(F(x), G(x), H(x)) =

Theorem 3: u(x) is more concave risk averse than v(x) on [a, b] if and only if TuTv, for all F(x) G(x) and H(x) such that G(x) is riskier than F(x), and F(x) first-degree stochastically dominates H(x).

Value is 400 Probability of total loss is .1 Expected Value is 360 Price of lock is 45 Probability of loss is reduced to .001 Expected value is 354.6 Expected ineffective expenditure on self-protection, (.001)(45) = .45 Change in the mean is 360 - 354.6 = 5.4

Strongly More Risk Averse Revisited [ 1] July 13, 2012 Liqun Liu Jack Meyer