Private mortgage insurers posted an impressive 26.5 percent increase in new insurance written during the third quarter of 2012, but four of the industry’s six active firms are gradually taking market share away from their rivals. Private MIs insured $51.76 billion in new mortgage originations during the third quarter, according to a new Inside Mortgage Finance ranking and analysis, making it the strongest quarter for the beleaguered industry since the second quarter of 2008. FHA and VA lending grew at a much slower pace, climbing just 2.1 percent and 4.0 percent, respectively, during the third quarter. The result was...[Includes two data charts]