How do you get borrowers to avoid walking away from homes that are deeply underwater without encouraging more to follow by writing down principal balances? One idea: Pay them to keep paying their mortgage. The novel approach is being touted by Loan Value Group LLC, a firm selling their idea—and ready-made application—to mortgage investors nervous about the risk of strategic default, where borrowers walk away from their homes even though they can afford to pay their mortgages.  The firm says it’s signed up an undisclosed mortgage investor to test a pilot program with a few hundred borrowers.