The use of absorbing boundaries in the analysis of bankruptcy

An explicit solution is given for the value of a risk neutral firm with stochastic revenue facing the possibility of bankruptcy. The analysis is conducted in continuous time. Uncertainty is modeled using an Ito process and bankruptcy is modeled as an absorbing boundary. The analysis yields an ordinary differential equation with a closed form solution. The value function is used to calculate the firm's demand for high interest rate loans, showing a positive demand at interest rates which appear intuitively to be excessive. A value function is also derived for a risk neutral lender advancing funds to the firm. The borrowing and lending value functions are then used to examine various aspects of lender-borrower transactions under different bargaining structures. In a competitive lending market, the model shows that credit rationing occurs inevitably. In a monopoly lending market, the lender sets interest rates and maximum loan levels which reduce the borrower to zero profit. When a second borrower is introduced, the lender must allocate limited funds between two borrowers. A lender is shown to squeeze the smaller "riskier" borrower out of the market when the lender's overall credit constraint is tight. Under each bargaining structure, the model is also used to examine changes in the respective "salvage" recoveries of the lender and borrower on bankruptcy. Accepted:Arts, Faculty ofVancouver School of EconomicsGraduat