American International Group (AIG 0.09%) reports its third-quarter earnings after the markets close Thursday. Since some of AIG's competitors have already reported, we can use their results as a loose guide for what to expect from AIG. For investors seelomg a bit of guidance on what to look out for, here are the top three areas you should focus on in the insurer's results.

1. Premiums growth
As one of my top criteria for evaluating an insurance company, premiums growth should always be something you look at in quarterly reports. Based on a few different facts, we should expect to see AIG report an increase in premiums due to rate increases. In a recent Towers Watson survey, the CFOs from 25 of country's top property and casualty insurance companies reported that they see the current market hardening, and expect it to remain that way for at least a year. With that in mind, it's not surprising that competitor Allstate (ALL -1.92%) reported a 4.1% increase in rates during the third quarter. AIG reported a similar rise in the second quarter, so you should expect to see continued increases.

2. Mortgage guaranty
In the past few quarters, there has been an explosion of new business in the mortgage-guaranty market. During the second quarter, AIG reported a 60%+ increase in new policies written following the big jump in new home loans. Based on two of AIG's competitors, however, we shouldn't expect the same level of gains in its third-quarter report. Genworth Financial (GNW -2.79%) reported a 36% increase in new insurance written versus the third quarter in 2012, but only a 2% increase versus the previous quarter. MGIC Investment (MTG -0.52%) meanwhile, reported a 22% increase in new insurance written versus 2012, but flat sequentially. Due to the seasonality of the housing market, as well as some small increases in interest rates, investors should expect to see similar results from AIG's private mortgage insurance division. Though it will likely still report a big jump from 2012's results, the sequential growth has a high probability of slowing down.

One other factor that investors should look at within AIG's mortgage guaranty operations is the continued burn-off of delinquencies from old policies. Both MGIC and Genworth Financial reported continued declines in delinquency rates, with most of the new business being written after 2009.

3. Investment income
Every insurance company has a great deal of sensitivity to interest rates, so it has been common practice for their investment managers to hedge against the low interest rate environment. With some increases in interest rates during the third quarter, investors should look at how the company is managing the challenges posed by changing rates. For example, Markel (MKL -1.50%) has increased its exposure to both residential and commercial mortgage-backed securities by more than 300% in the past year in order to increase its portfolio's yield. AIG has likewise increased its exposure to alternative investments in the past few quarters. Keep an eye out for further changes, as this will tell you the direction that management believes the market is moving (i.e., continued increases in rates).

Bonus!
With all of these items to watch for, you may think that you have enough on your plate. But be on the lookout for more information on the company's plans for its International Lease Finance Corp. Though it has yet to announce that its outstanding deal with a Chinese consortium is dead, AIG has been shopping around the idea of an IPO for the aircraft leasing business. Any new developments could lead to a boost in the company's share price since International Lease Finance carries the bulk of AIG's remaining debt burden and investors are anxious to see it sold or spun off.

Another good quarter?
Earnings season is one of the best times to take stock in your portfolio and re-evaluate the companies you've chosen. Though the Motley Fool promotes a long-term outlook, each quarter gives you the chance to make sure that the investments you've made still stack up to your original investment thesis. For AIG investors, or those interested in jumping in, this quarter should give you a good sense of how the company is managing its challenges and hot streaks -- and it's helpful to know how it deals with both.