Stock indices in the U.S.A. and Asia mostly advanced and their gains were broadly driven by hopes that recent proposals by Greek PM Alexis Tsipras will help Greece and its international lenders come to an agreement.

So far there is no deal and no official statements about it, but some positive remarks made by European policymakers after yesterday's summit spurred optimism among market participants.

The Dow Jones industrial average rose by 103.83 points, or 0.58%, to 18,019.78. The Standard & Poor's 500 rose by 12.86 points, or 0.61%, to 2,122.85 (health-care companies gained 0.8%). The Nasdaq Composite gained 36.97 points, or 0.70%, to close at record 5,153.97.

In Asia Hong Kong Hang Seng rose by 0.56%, or 151.36 points, to 27,232.21. China Shanghai Composite Index declined by 0.09%, or 3.91 points, to 4,474.46. Meanwhile the Nikkei rose by 1.53%, or 311.98 points, to 20,740.17.

The Shanghai index continued last week's correction caused by liquidity concerns as new curbs on margin financing and new-share listings weighed on liquidity.