Mainly focusing on life insurance and pensions, in the face of mature markets and strong competition at home.
Rapid economic growth in countries such as Ghana, Kenya and Nigeria has increased the number of people with money to spend on insurance to protect their wealth, while regulatory changes are encouraging the growth of domestic savings and pensions.
Several major companies, including Swiss Re, Prudential and Sanlam, are buying insurers in Africa, with the focus on life and pension products in the more economically advanced sub-Saharan countries.
(READ MORE: Sanlam penetrates Rwanda's insurance market)
Notwithstanding the challenges, the race is definitely on. David Hodnett, Barclays Africa's deputy CEO, told a banking conference in Johannesburg in November: "Every insurer that you look at has probably about five or six suitors."
A Standard Bank report published in August said while the size of the "middle class" in sub-Saharan Africa may have been overstated in some studies, growth rates were nevertheless dramatic.
Its study of 11 sub-Saharan economies concluded the "middle class" had risen from 4.6 million to 15 million since 2000 and would be over 40 million by 2030, with Africa's biggest economy Nigeria leading the way.
Insurance penetration, or premiums written as a percentage of gross domestic product, was 11.5 per cent in Britain in 2013 but just 0.6 per cent in Nigeria. For life insurance, penetration was 8.8 per cent versus 0.2 per cent, according to Swiss Re data.
Life insurance premium volume in dollar terms rose 18.6 per cent last year in Kenya, 13.8 in Angola and 13.5 in Nigeria, compared with a 3.9 per cent rise in Britain, the data showed.
"The level of life products and penetration is very low," said Davinder Sikand, head of Africa at private equity firm Abraaj. "There are a lot of opportunities to develop products to fit the needs of the people."
One of the latest deals was French insurer AXA's 250 million US dollar purchase last month of a majority stake in Nigeria's Mansard Insurance, which offers life and general insurance.
(READ MORE: Kenya's life insurance industry on the upswing)
South Africa-focused companies such as Old Mutual and Liberty are also eager to expand in the life market in sub-Saharan Africa.
LeapFrog Investments, which invests in financial services in emerging markets, launched its second Africa and Asia fund in September while British insurer Prudential has bought life insurers in Kenya and Ghana this year.
HARD TO REACH
Insurance specialists say middle-class and lower middle-class customers in Africa are not as affluent as developed-world middle classes, tend to be harder to reach and can require a larger use of face-to-face agents.
The numbers in the Standard Bank survey are based on households that consume more than 15 US dollars a day.
A shortage of skilled insurance staff, fragmentation of the market across a large number of countries with many small insurance firms and regulatory hurdles present more obstacles.
"It's quite challenging, a lot of work is required," said Frank O'Neill, head of Middle East and Africa at Swiss Re. "It's not as straightforward as if you look at Brazil: one single country."
Getting regulatory approval can take more than a year for each new company bought, and frameworks differ from country to country, industry specialists say.
"Wherever you go there are new regulations to learn and comply with," said Victor Muguto, head of insurance for consultancy PwC in Africa.
"There are shortages of staff in some of the countries, experienced staff are not always easy to come by," he said.
Would-be insurance buyers will also need to do their homework to work out which of the many local insurers offer the most value. Profits across the board in Kenya's insurance sector, for example, rose 24 per cent last year, but that covers nearly 50 companies.
Insurers are more likely to do well if they partner with banks, said Dudu Tembo, portfolio manager at wealth manager Citadel Investment Services, as "the challenge has been issues around distribution".
Reinsurance, or sharing the burden of insurance risk, is another growth area, for instance for energy projects in countries such as Angola or Mozambique. An Africa-focused reinsurance company, One Re, launched last month.