| Abstract: |
| In this paper, we extend the optimal securitisation model of Pag\`{e}s and Possama\{i} and Pag\`{e}s between an investor and a bank to a setting allowing both moral hazard and adverse selection. Following the recent approach to these problems of Cvitani\`{c}, Wan and Yang, we characterise explicitly and rigorously the so-called credible set of the continuation and temptation values of the bank, 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 Nicol\`{a}s Hern\`{a}ndez Santib\`{a}\~{n}ez and Dylan Possama\{i}. |
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