Game-theoretical models of debt and bankruptcy

The talk will be concerned with problems of optimal debt management. In a basic model, the interest rate as well as the bankruptcy risk are given a priori. In this case the borrower faces a standard problem of optimal control.
In alternative, debt management can be modeled as a noncooperative game between a borrower and a pool of lenders, in infinite time horizon with exponential discount. The yearly income of the borrower is governed by a stochastic process. When the debt-to-income ratio surpasses a given threshold, bankruptcy occurs.
The interest rate charged by the risk-neutral lenders is precisely determined in order to compensate for this possible loss of part of their investment.
Existence and properties of optimal feedback strategies for the borrower will be discussed, in a stochastic framework as well as in the limit deterministic setting.