After approximately $4.5 billion paid out to victims of BP’s record-breaking Gulf of Mexico oil spill, the company is urging U.S. officials with the Gulf Coast Claims Facility to halt further compensation.

Citing an improving Gulf coast economy, the British oil giant said in a 29-page letter (PDF) released to the press that it does not expect any more residents or businesses to “incur a future loss related to the oil spill.”

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“Multiple lines of evidence demonstrate that, to the extent that portions of the Gulf economy were impacted by the spill, recovery had occurred by the end of 2010, and that positive economic performance continues into 2011, with 2011 economic metrics exceeding pre-spill performance,” the company added.

The only exception made was for oyster farmers who are able to prove the company’s pollution destroyed their oyster beds.

Despite BP’s rosy outlook on the future of its Gulf damage payments, many fishermen claim to still be experiencing the spill’s ill-effects, with harvests of crab and oysters plunging significantly over last season.

About 195,000 claims have been paid through the company’s $20 billion fund, overseen by U.S. officials. The fund’s administrator, Ken Feinberg, said in a prepared statement that he welcomes all input on “advisement,” but made no comment on whether payments would stop.