I don't mean explorers of the Americas like Columbus, Vespucci or Cabot. I'm interested how people (like Ernest Shackleton) managed to get to Antarctica, the interior of Africa and the jungles of India. Were the trips paid for by the state? Did they use their own wealth?
Shackleton appears to have sought government funding, but when that fell through he turned to private capital.
His friend John Rowett aided him in raising funds for his 1922 expedition. The mention here is in passing, but does elaborate on the voyage.
For his 1914 expedition James Wordie helped him purchase fuel for his ship. Again, the mention is fleeting, but here is the link
The most detailed breakdown I can find comes from Wikipedia
Shackleton used his considerable fund-raising skills, and the expedition was financed largely by private donations, although the British government gave £10,000 (about £680,000 in 2008 terms). Scottish jute magnate Sir James Caird gave £24,000, Midlands industrialist Frank Dudley Docker gave £10,000 and tobacco heiress Janet Stancomb-Wills gave an undisclosed but reportedly "generous" sum.
Some link mining shows that that information is drawn from this book. It seems inline with the other information I could find but the author has written a number of polemics on Antarctic exploration so I would be careful.