This answer contains spoilers for Captain America: The Winter Soldier, Avengers: Age of Ultron, Ant-Man and Agents of SHIELD.
"Cut off one head and two more shall take it's place".
One of the problems of fighting Hydra is that whenever you oust one of their leaders, a power vacuum forms in which one or more other versions of Hydra will form.
We've seen this at least twice in the Marvel Cinematic Universe now - once after Alexander Pierce was killed in Captain America: The Winter Soldier, which led to Baron von Strucker (Avengers: Age of Ultron) and Daniel Whitehall (Agents of SHIELD) getting promotions, and then again since the death of these two characters, which seems to have resulted in Grant Ward (Agents of SHIELD) and Mitch Carson (Ant-Man) gaining power.
It is this character, Mitch Carson, who seems to be in charge of Hydra in Ant-Man, but we can see from other areas of the MCU that this is just once of at least two Hydra cells operating at the moment. Thanks to how high up Carson was in SHIELD before it fell, I wouldn't be surprised to learn that he is the leader of his Hydra.
As for the issue of money - we know that Hydra had ties to both SHIELD and the US Senate before they were discovered. Although Senator Stern was arrested in the wake of the Fall of SHIELD, we see in Ant-Man that Mitch Carson (a very high up person in SHIELD) is still on the loose, so we can be fairly certain that Hydra must still contain rich and powerful people in order to fund them - such as the wealthy son of Baron von Strucker, who was recently introduced into Agents of SHIELD.
Update: 05/11/2015 - As per last nights episode of Agents of SHIELD "Among Us Hide...", it would seem that there is yet another Hydra faction out there somewhere that has been around for at least some time. It remains to be seen if this faction has links to the Mitch Carson faction from Ant-Man, or any of the other factions we have seen in the Marvel Cinematic Universe so far.
Update: 11/03/2016 - The faction of Hydra mentioned above ended up having no links to the faction seen in Ant-Man, at least as far as I can tell. Additionally, a recent episode of Agents of SHIELD saw SHIELD taking out all the Hydra bases in the world; it remains to be seen if this is truly the end of Hydra, or if new heads will grow. Given the organisations history, I'd wager on the latter.