A Mathematical Treatment of Bank Monitoring Incentives

38 Pages Posted: 15 May 2012

Date Written: April 1, 2012

Abstract

In this paper, we take up the analysis of a principal/agent model with moral hazard, with optimal contracting between a competitive investor and an impatient bank monitoring a pool of long-term loans subject to Markovian contagion. We provide here a comprehensive mathematical formulation of the model and show using martingale arguments in the spirit of Sannikov how the maximization problem with implicit constraints faced by investors can be reduced to a classic stochastic control problem. The approach has the advantage of avoiding the more general techniques based on forward-backward stochastic differential equations and leads to a simple recursive system of Hamilton-Jacobi-Bellman equations. We provide a solution to our problem by a verification argument and give an explicit description of both the value function and the optimal contract. Finally, we study the limit case where the bank is no longer impatient.

Keywords: Default Correlation, Dynamic Moral Hazard, Forward-Backward Stochastic Differential Equations

JEL Classification: G21, G28, G32

Suggested Citation

Pages, Henri F. and Possamaï, Dylan, A Mathematical Treatment of Bank Monitoring Incentives (April 1, 2012). Banque de France Working Paper No. 378, Available at SSRN: https://ssrn.com/abstract=2060103 or http://dx.doi.org/10.2139/ssrn.2060103

Henri F. Pages (Contact Author)

Banque de France ( email )

DGEI 49-1431
Paris Cedex 01, 75049
France
+33 1 42922999 (Phone)
+33 1 42924937 (Fax)

Dylan Possamaï

ETH Zürich ( email )

Raemistrasse 101
Raemistr. 101
Zurich, 8092
Switzerland

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