United Guaranty, the largest private mortgage insurer in the nation, filed to go public this week, touting its market position, longevity and the strong profits it posted over the past two years. Then again, it’s been a tough market for mortgage-related stocks this year. Overall, United Guaranty hopes to raise $100 million by selling 19.9 percent of the firm, with its parent company, American International Group, retaining the balance while setting the stage for eventual ...