TORONTO, Nov 5 (Reuters) - Sun Life Financial is considering a range of options to expand in Asia, including buying insurance and asset management firms and taking bigger stakes in existing joint venture partners, Chief Executive Dean Connor said on Thursday.

In the United States, Canada's second-largest life insurer is seeking opportunities to add group benefits and stop-loss businesses to expand on its offerings in those areas, Connor said on an analyst call.

On Wednesday, Sun Life reported third-quarter core earnings of C$1.44 a share, beating analyst expectations of C$1.28, helped by growth in its Asia and asset management businesses.

Its shares rose 2.9% to C$56.51 on Thursday, compared with a 1.7% gain in the Toronto stock benchmark.

""Asia has gone from 7% of our earnings to closer to 20% in this quarter," Connor said in an interview. "In my mind, there's no doubt that... at some point, it'll be 25% or more."

The company has deliberately chosen markets in Asia that have "significant runway to grow" and is avoiding more mature countries like Japan, South Korea and Taiwan, he said.

Sun Life's U.S. unit posted a loss in the three months through September, albeit narrower than a year ago, and executives acknowledged the stop-loss policy business - which protects against large claims - is highly competitive.

But it is one of the biggest contributors to Sun Life's U.S. growth, and the company is seeking to grow the business, they said.

From a historical focus primarily on high-claim risk protection, "we'd like to step further into the health care space, providing care management, navigation-type services to the members we work with," Daniel Fishbein, president of Sun Life U.S., said on the call. (Reporting By Nichola Saminather Editing by Marguerita Choy)