Batman: Under the Red Hood

At his manor, Ra's al Ghul realizes his mistake in allying with the Joker and using him as a distraction for the Dynamic Duo while Ra's himself tried to cripple the economy of Europe by destroying its financial districts. Meanwhile, in Sarajevo, Bosnia, the Joker has kidnapped Jason Todd, the second Robin, and brutally beats him with a crowbar in an abandoned warehouse. The Joker then leaves Jason locked in the warehouse with a bomb. Batman arrives too late as the warehouse explodes, killing Jason.
Five years later in Gotham City, a vigilante criminal called Red Hood assembles a meeting with the city's most notorious thugs and dealers. He announces his takeover of their drug trade, telling them that he will get 40% of the profit, and they will get total protection from both Black Mask, the reigning kingpin of the Gotham underworld, and Batman. However, he warns them not to deal to children, threatening to kill them if they do. Elsewhere, Batman stops an attempted theft of a shipment belonging to Black Mask, revealed to be Amazo. Batman destroys Amazo with the help of Nightwing. Interrogating the thieves, Batman learns they are working for Red Hood before Red Hood himself kills them. Batman chases Red Hood who leads him to Ace Chemicals - the site of the first Red Hood's transformation into the Joker - and then sets off an explosion that destroys the facility with Batman barely escaping.
Batman and Nightwing go to Arkham Asylum to interrogate the Joker about Red Hood. He merely taunts Batman about Jason's death, then denies any involvement with his successor. Meanwhile, Black Mask, enraged that Amazo was destroyed, has his assistant Ms. Li put a hit on Red Hood. After learning of Black Mask's next shipment, Red Hood hijacks the helicopter carrying it, but is stopped by Batman and Nightwing. Red Hood flees and Batman and Nightwing pursue him. During the chase, Red Hood performs maneuvers similar to Batman's and Nightwing's, also cutting one of Batman's cables with a knife. The chase ends at a train station, where Red Hood escapes after detonating a bomb that injures Nightwing. In the Batcave, Batman reviews audio footage of the chase, which reveals that Red Hood knows his secret identity. He then recalls Jason performing the same maneuvers he saw Red Hood use. In addition, a flashback reveals that as he got older, Jason grew darker and more violent and brutal, once even going so far as to break a criminal's collar bone in a fight.
In the present day, the Fearsome Hand of Four consisting of their leader, Baton, Bulk, and Shot lure out Red Hood by attacking Tyler Bramford, a criminal under his protection. They nearly overpower him with their leader cutting him on the shoulder. Batman then appears and helps Red Hood battle the group. They incapacitate three, but Batman is horrified when Red Hood kills Shot with a taser. After having an argument over how best to fight crime, Batman tries offering Red Hood help, but Red Hood rebuffs his attempts to help and leaves. Batman obtains a blood sample of Red Hood off one of the assassin's swords. The analysis shows it is a match for Jason. After exhuming the body and finding it to be a fake, Batman leaves to interrogate Ra's al Ghul. After surviving an assassination attempt by Red Hood, Black Mask reluctantly decides to set the Joker free from Arkham Asylum and give him the task of killing Red Hood.
Meanwhile, Batman confronts Ra's al Ghul at his mansion and demands to know the truth about Jason. Ra's al Ghul admits that he felt responsible for Jason's death, which was not part of his agreement with the Joker, and decided not to make war with Batman anymore; as a peace offering, he swapped Jason's body for a fake and revived him in his Lazarus Pit. Following his resurrection however, Jason was seemingly driven insane and escaped by leaping off a cliff. Ra's and his men believed Jason to have been killed in the fall, but deduces that recent events have since proved otherwise.
On his way back to Gotham City, Batman finds that the Joker has abducted Red Hood's crime bosses as well as Black Mask. As the Joker tries to set his hostages on fire, Red Hood appears and reveals that the Joker is his real target. Batman saves the hostages and tries to take the Joker with him, but Red Hood abducts him first, instructing Batman to come to Crime Alley if he wishes to reclaim him. At an abandoned apartment, Red Hood brutally beats the Joker with a crowbar, in revenge for his own murder, and then later confronts Batman. During the fight, Red Hood removes his helmet, confirming that he truly is Jason Todd.
Fleeing back to the apartment, Jason holds Batman at gunpoint and tells him that he forgives him for not saving him, but angrily confronts him over his decision to still allow the Joker to live. Batman confesses that he has always wanted to kill the Joker, but will not allow himself the pleasure out of fear of fully succumbing to it. Jason then tosses Batman a gun and gives him an ultimatum: Jason will execute the Joker unless Batman shoots him to prevent it, much to the Joker's pleasure. Batman refuses and drops the gun. Angered, Jason shoots at Batman, but Batman dodges the bullet and throws a batarang into the barrel of the gun, causing a small explosion that mangles Jason's gun hand. Defeated and critically injured, Jason uses his other hand to set off a time bomb he had previously planted in the room. Wanting them all to die together, the Joker maniacally delays Batman long enough to stop him from defusing the bomb. Batman subdues the Joker and leaves him for dead in an attempt to rescue Jason. The bomb goes off and while Batman and the Joker survive the explosion, Jason is nowhere to be found, leaving his fate ambiguous.
In the aftermath, the Joker is returned to Arkham Asylum, and Black Mask is arrested by the police where he is awaiting trial for his alleged involvement in the Joker's escape. Back at the Batcave, Alfred asks Batman if he should remove the memorial display case containing Jason's Robin uniform. Batman replies that nothing has changed and departs in the Batmobile. A flashback is then shown of Jason's first day in his Robin costume, which he declares is the best day of his life.

Question: What happens to Jason after the bomb went off?
Answer: his fate is ambiguous