A captive insurer is a method for aggregating risks within a corporate group. The captive insurer then has access to reinsurance markets. Yes, Jupiter is a wholly owned subsidiary of BP, but jupiter has a balance sheet in its own right, with its own capital and its own reserves for outstanding claims and unearned premium - like any insurer does.
Jupiter is reported to have a USD700mil net retention (the self insured component) and it will be capitalised to withstand this degree of loss (i.e. the money will already be in the insurer). Any costs in excess of USD700mil will fall to reinsurers. In short, reinsurance markets will take a bath on this and that will have implications for the global insurance industry. The property and third party liability losses will be nothing compared to the business interruption component of the claim that BP will seek to recover from Jupiter (and jupiter will then in turn seek to recover from reinsurers).
The biggest issue that Jupiter (and therefore BP) will face is one of liquidity. In situations like this, the captive and the reinsurers will have looooong disputes about the actual size of the claim and the terms upon which the claims are paid. They wont know the costs until its all done and dusted.
This means that Jupiter may face significant delays in recovering from reinsurers, yet it will be paying claims to BP group entities in the meantime and it needs to be able to withstand the difference in the timing of these payments.