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The researchers have developed a new model that can help shipowners and ship designers make good decisions in a time of great uncertainty.

The legal wrangling began this week when the shipowner, Grace Ocean Private Ltd., and the ship manager, Synergy Marine, both based in Singapore, filed a petition in U.S.

The lucrative trade is believed to have earned the shipowners a lot of money.

Given Russia’s withdrawal from the deal that guaranteed safe passage for commercial vessels through the Black Sea, insurance premiums are likely to be prohibitively expensive for shipowners, analysts said.

They already cost thousands of dollars and are expected to go up, while shipowners could prove reluctant to allow their vessels to enter a war zone without Russia's agreement.