U.S. stocks closed a bit higher Thursday, as investors continue to eye Greece after the struggling country submitted reform proposals to Eurogroup officials. Global markets have remained on edge this week due to volatility in Asia's stocks, as Athens inches closer to bankruptcy. 

The Dow (INDEXDJX:.DJI) gained 33.20 points, or 0.19 percent, to close at 17,548.62. The S&P 500 index (INDEXSP:.INX) added 4.63 points, or 0.23 percent, to end at 2,051.31. And the Nasdaq Composite (INDEXNASDAQ:.IXIC) rose 12.64 points, or 0.26 percent, to finish at 4,922.40.

U.S. equities traded higher Thursday, with the Dow Jones Industrial Average soaring more than 230 points in morning trading after equities in Asia rebounded following a sharp sell-off a day earlier. Seven out of the 10 S&P 500 sectors closed higher, led by gains in the financial sector, up nearly 1 percent, while the utilities sector was the biggest loser down just over 1 percent.

Property and casualty insurer Travelers Companies Inc. (NYSE:TRV) led the Dow higher Thursday, adding more than 1 percent, while iPhone maker Apple Inc. (NASDAQ:AAPL) and chip maker Intel Corporation (NASDAQ:INTC) were the biggest decliners in the index, both down 2 percent.

Global stocks have seen volatile swings this week, with extreme volatility ripping through China’s stock markets. The Shanghai Stock Exchange Composite index jumped 6 percent Thursday, rebounding from a sharp selloff the previous session after the index tumbled more than 30 percent from its peak in mid-June.

Meanwhile, Greece is seeking a third bailout, totaling 53.5 billion euros ($59 billion) from its international creditors as part of a new bailout package, The Associated Press reported.

Under the new reform proposals, Greece said it would undertake austerity measures worth between 12 billion and 13 billion euros ($13 billion to $14 billion), including raising taxes on cafes, bars and restaurants, The Washington Post reported. And Greece would reform its pension program. The value-added tax rate for restaurants and catering would be 23 percent, while hotels would be 13 percent, Reuters reported. 

The Greek proposal set a primary surplus target of 1 percent this year and 2 percent in 2016, CNBC reported. Greece's Parliament is expected to vote on the draft Friday, and Eurogroup officials are scheduled to meet Sunday to review the new reforms.

Investors' sentiments have waned this week as Athens teeters on the brink of exiting the 19-member eurozone. The country rejected international creditors' demands in a referendum Sunday, following a default to the International Monetary Fund last week. Certain pension benefits gradually would be phased out by the end of 2019, Reuters said.

Experts say that with China’s benchmark index starting to improve, there may even be relief if the uncertainty over Greece’s membership in the eurozone is finally resolved.

“While global equities and commodities might weaken a little further, they have already been undermined by a combination of ‘Grexit’ and China fears, so the downside from here should now be limited,” Julian Jessop, chief global economist at Capital Economics, said in a research note Thursday.