I present alternative constructions of gambles with greater risk. Rothschild and Stiglitz (1970) demonstrate that gamble Y has greater risk than X when Y is equal in distribution to X Z, where Z is noise. Gambles called positive-upper-conditional-mean errors are introduced, and I show that Y has...

I present a theory of financial contracts that transfer risk from one party to another. Risk reduction is equivalent to adding inside noise to payoffs; this addition shifts probability weight away from the tails of a payoff's distribution. Adding outside noise is the inverse operation and it...