Bank Monitoring Incentives Under Moral Hazard and Adverse Selection

Abstract

In this paper, we extend the optimal securitisation model of Pagès [50] and Possamaï and Pagès [51] 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 [14], 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.Principal-Agent problems with moral hazard have an extremely rich history, dating back to the early static models of the 70s, see among many others Zeckhauser [68], Spence and Zeckhauser [63], or Mirrlees [42,43,44,45], as well as the seminal papers by Grossman and Hart [26], Jewitt, [33], Holmström [30] or Rogerson [57]. If moral hazard results from the inability of the Principal to monitor, or to contract upon, the actions of the Agent, there is a second fundamental feature of the Principal-Agent relationship which has been very frequently studied in the literature, namely that of adverse selection, corresponding to the inability to observe private information of the Agent, which is often referred to as his type. In this case, the Principal offers to the Agent a menu of contracts, each having been designed for a specific type. The so-called revelation principle, states then that it is always optimal for the Principal to propose menus for which it is optimal for the Agent to truthfully reveal his type. Pioneering research in the latter direction were due to Mirrlees [46], Mussa and Rosen [47], Roberts [55], Spence [62], Baron and Myerson [7], Maskin and Riley [38], Guesnerie and Laffont [27], and later by Salanié [59], Wilson [67], or Rochet and Choné [56]. However, despite the early realisation of the importance of considering models involving both these features at the same time, the literature on Principal-Agent problems involving both moral hazard and adverse selection has remained, in comparison, rather scarce. As far as we know, they were considered for the first time by Antle [2], in the context of auditor contracts, and then, under the name of generalised Principal-Agent problems, by Myerson [48] 1 . These generalised agency problems were then studied in a wide variety of economic settings, notably by Dionne and Lasserre [17], Laffont and Tirole [35], McAfee and McMillan [39], Picard [54], Baron and Besanko [4, 5], Melumad and Reichelstein [40, 41], Guesnerie, Picard and Rey [28], Page [49], Zou [69], Caillaud, Guesnerie and Rey [10], Lewis and Sappington [36], or Bhattacharyya [8] 2 .All the previously mentioned models are either in static or discrete-time settings. The first study of the continuous time problem with moral hazard and adverse selection was made by Sung [64], in which the author extends the seminal finite horizon and continuous-time model of Hol...

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A continuous-time model of self-protection

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