In this paper, we extend the optimal securitization model of Possamaï and Pagès
between an investor and a bank to a setting allowing both moral hazard and
adverse selection. Following the recent approach to these problems of Cvitanić,
Wan and Yang, we characterize explicitly and rigorously the so-called credible set
of the continuation and temptation values of the banks, and obtain the value
function of the investor as well as the optimal contracts through a recursive
system of first-order variational inequalities with gradient constraints. We provide
a detailed discussion of the properties of the optimal menu of contracts. This is a
joint work with Nicolás Hernández Santibáñez and Dylan Possamaï.