We analyze recently proposed mortgage contracts that aim to eliminate selective borrower default when the loan balance exceeds the house price (the ``underwater'' effect). We show contracts that automatically reduce the outstanding balance in the event of house price decline remove the default...

We derive a simple integral equation for the default probability over a finite time horizon of a company that makes coupon payments on its debt and infrequently returns to its leverage target by increasing its debt unless it defaults on its debt. Compared to the conventional (constant default...