The terms asset lease and finance lease are used interchangeably. An asset lease exists where the ownership of the vehicle is held by the lessor (finance company) and is permitted for use by the lessee (borrower) for a set monthly fee. At the end of the lease term the vehicle ownership transfers to the lessee (borrower). This may or may not involve a final residual payment paid to the lessor (finance company). During the lease term the lessor would claim depreciation on the vehicle, and the lessee would claim the leasing expense as a tax deduction.