* The Doctors Co offers $41.50 per American Physician share
* Offer represents 31 pct premium
* American Physicians shares up 34 pct
July 8 American Physicians Capital Inc ACAP.O agreed to be bought by a private insurer and a physician and surgeon medical liability, for about $386 million, sending its shares up 34 percent.
Shares of the healthcare liabilities provider touched a new life-high at $42.455 Thursday on Nasdaq, surpassing the offer price.
The $41.50 per share offer from The Doctors Co of American Physicians represents a 31 percent premium to the stock's closing price of $31.76 Wednesday.
The deal expands the private firm's position as the largest national insurer of physician and surgeon medical liability to nearly 55,000 insured members, American Physicians said in a statement. American Physicians' board approved the offer and the deal is expected to close in the fourth quarter of 2010.
Shares of the company were up 28 percent at $40.66 in afternoon trade Thursday on Nasdaq. (Reporting by Vidya L Nathan in Bangalore; Editing by Gopakumar Warrier)