Risk aversion recovered from an optimal two-state payoff
= Risk aversion recovered from an optimal two-state payoff
{title2=$R=\log(Z_u/Z_d)/\log(W_d/W_u)$}
For an interior optimal payoff in a complete two-state market under <CRRA utility>, $W_u^{-R}/W_d^{-R}=Z_u/Z_d$. If the two positive payoffs differ, taking logarithms gives the displayed coefficient. The multiplier can then be recovered from either state. A positive coefficient requires the price-density and payoff orders to be compatible with decreasing marginal utility.