  We consider the problem of Adverse Selection and optimal derivative design
within a Principal-Agent framework. The principal's income is exposed to
non-hedgeable risk factors arising, for instance, from weather or climate
phenomena. She evaluates her risk using a coherent and law invariant risk
measure and tries minimize her exposure by selling derivative securities on her
income to individual agents. The agents have mean-variance preferences with
heterogeneous risk aversion coefficients. An agent's degree of risk aversion is
private information and hidden to the principal who only knows the overall
distribution. We show that the principal's risk minimization problem has a
solution and illustrate the effects of risk transfer on her income by means of
two specific examples. Our model extends earlier work of Barrieu and El Karoui
(2005) and Carlier, Ekeland and Touzi (2007).
