Optimal Consumption and Investment with Bankruptcy

The book delves into advanced continuous-time consumption investment models, building on the foundational work of Robert Merton and Paul Samuelson. It features critical analyses, particularly by Karatzas, Lehoczky, Sethi, and Shreve, who reexamine Merton's model using modern mathematical techniques. Their findings indicate that Merton's solutions may not hold under certain conditions, particularly regarding constraints on negative wealth and consumption. Subsequent analyses by Sethi and Taksar further explore these issues, providing a comprehensive critique of existing models.