A Differential Game of Debt Contract Valuation

Abstract

This paper deals with a problem of uncertainty management in corporate finance. It represents, in a continuous time setting, the strategic interaction between a firm owner and a lender when a debt contract has been negotiated to finance a risky project. The paper takes its inspiration from a model by Anderson and Sundaresan (1996) where a simplifying assumption on the information structure was used. This model is a good example of the possible contribution of stochastic games to modern finance theory. In our development we consider the two possible approaches for the valuation of risky projects: (i) the discounted expected net present value when the firm and the debt are not traded on a financial market, (ii) the equivalent risk neutral valuation when the equity and the debt are considered as derivatives traded on a spanning market. The Nash equilibrium solution is characterized qualitatively.