Worldwide insurance premiums will grow by around 4.5 percent in nominal terms - unadjusted for inflation - this year and next, up from 3.0 percent in 2016, the group predicts in a study.
In real, inflation-adjusted terms, that would see insurers' revenue grow 2.9 percent this year and 3.1 percent in 2018, roughly keeping pace with global economic growth.
Munich Re expects premiums to reach some 4.56 trillion euros ($4.9 trillion) in absolute terms in 2018, up from 4.18 trillion last year.
"The economies of many emerging markets, such as Brazil, but even Russia, are experiencing a significant recovery," the group's chief economist Michael Menhart said in a statement.
"This is leading to increased growth in property-casualty insurance." "Solid" economies in Europe, Japan and the US were also supporting demand, he went on.
Menhart expects the growth to balance out negative factors, such as slowing economic expansion in China.
Looking further ahead, emerging Asian economies will boost their share of global insurance premiums to 21.4 percent by 2025 from today's 13.3 percent, Munich Re predicts - not far short of western Europe's anticipated 24.5-percent market share.
Emerging economies in Asia and Latin America are driving growth in demand for life insurance, a sector facing headwinds from low interest rates in advanced economies.
Life insurance premiums are expected to expand by 3.0 percent in real terms by 2018, slightly faster than global growth.
Meanwhile, property and casualty insurance will grow by 2.5 percent, with strong support from Asia, Africa and the Middle East.
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