The Cayman Islands Monetary Authority (CIMA) has published statistics for the numbers of private investment funds registered with them across various categories and in aggregate (typically excluding PE and VC) as at the end of 2018. To view the statistics click here. (http://www.cima.ky/investment-statistics)
The statistics show some modest growth: across all categories (aggregated) an increase of almost 1% from end of Q3, 2018, and up 4% from the number at this time last year. The total at end of 2018 is 10,992.
Breaking the numbers down, CIMA report an increase of 1% in the registered category, 1% for master funds and no change for administered funds.
Note: the CIMA do not monitor or publish statistics for those sub-15 investor funds which are structured as unregulated products.