Date of Award
8-1-2012
Degree Name
Doctor of Philosophy
Department
Mathematics
First Advisor
Mohammed, Salah-Eldin
Abstract
We suppose that the price of a firm follows a nonlinear stochastic delay differential equation. We also assume that any claim whose value depends on firm value and time follows a nonlinear stochastic delay differential equation. Using self-financed strategy and replication we are able to derive a random partial differential equation (RPDE) satisfied by any corporate claim whose value is a function of firm value and time. Under specific final and boundary conditions, we solve the RPDE for the debt value and loan guarantees within a single period and homogeneous class of debt. We then analyze the risk structure of a levered firm. We also evaluate loan guarantees in the presence of more than one debt. Furthermore, we perform numerical simulations for specific companies and compare our results with existing models.
Access
This dissertation is Open Access and may be downloaded by anyone.