New York’s American International Group said its third-quarter net income rose 17 percent as its core insurance business improved. But its property and casualty unit still paid out more in claims than it took in, hitting shares. The insurer earned $2.17 billion, or $1.46, for the period, up from $1.86 billion, or $1.13, a year earlier. AIG received the biggest bailout of the financial crisis five years ago. It has repaid the federal government and has undergone a massive restructuring that cut its size in half. AIG also said it named Monika M. Machon treasurer, effective immediately.