Greek Prime Minister Alexis Tsipras and U.S. President Donald Trump shake hands at the start of a joint press conference in the Rose Garden of the White House in Washington, U.S., October 17, 2017. Kevin Lamarque | Reuters

Port of Piraeus, the largest port in Greece and one of the largest in the Mediterranean Sea Giorgos Georgiou | NurPhoto | Getty Images

Building investment ties

It is expected that Trump and Tsipras will examine ways to open the spigot on U.S. capital flows to Greece. Right now the United States is the sixth-largest foreign investor in Greece, an indebted nation trying to pull itself out of a severe depression for a decade. Despite falling back into recession in the first quarter, the economy is projected to expand by 1.8 percent this year and 2.6 percent in 2018, the IMF reports. And the IMF and other Greek creditors are drawing closer to a deal over the country's €86 billion program (US$101 billion), following parliament's approval of additional tax and pension reforms for the recently completed second evaluation of the Greek program.

The aircraft carrier USS Harry S. Truman arrives in Souda Bay, Crete. Mass Communication Specialist 3rd Class Cayman Santoro | U.S. Navy | Reuters

During last week's annual World Bank and IMF meeting, the Greek premier worked to secure a more flexible stance by the IMF to ensure that a third bailout review is completed by the end of this year and that Greece remains on track to exit the bailout next summer. The Greek prime minister's objective is to regain full market access to international bond markets and to leave institutional help behind. In July, Greece dipped into bond markets after a three-year hiatus, issuing five-year debt at an average yield of 4.66 percent. Greece is expected to return to the bond market again in the next 12 months.

People are still worried about the volatility, although the Greek economy is much better. Diego Ferro co-chief investment officer, Greylock Capital Management

Already there have been signs that U.S. investors are more willing to take on Greek risk. Calamos Investments' recent acquisition of Ethniki Insurance, Greece's largest insurance company, was a vote of confidence in the economic turnaround. The deal for a 75 percent stake in the insurer — a subsidiary of the National Bank of Greece — was made in June through a consortium of Calamos and Exin Partners. Calamos Investments is a global investment firm with more than $20 billion of assets under management. Exin is a Dutch investor focused on insurance, reinsurance and asset management.