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 Q1, 2018. (http://www.cima.ky/investment-statistics)
The statistics show continued stability: across all categories (aggregated) a fall of 0.08% (in context that is only 9 funds down from the year end), the total at end-Q1 is 10,500 which is a gain of 0.35% as compared to end-Q1, 2017. Breaking the numbers down, CIMA report marginal decreases of 0.5% in the registered category, -0.2% for master funds and -3% for administered funds.
Note: the CIMA do not monitor or publish statistics for those sub-15 investor funds which are structured as unregulated products.