COMMITMENTS AND CONTINGENCIES
We have certain noncancelable operating lease commitments with lease terms greater than one year for property and computer equipment. The minimum commitments under these agreements at December 31, 2018, were as follows: 
(millions)
Commitments

2019
$
64.1

2020
65.5

2021
52.8

2022
24.3

2023
8.5

Thereafter
3.8

Total
$
219.0


Some of the leases have options to renew at the end of the lease periods. The expense we incurred for the leases disclosed above, as well as other operating leases that may be cancelable or have terms less than one year, was: 
(millions)
Expense

2018
$
77.3

2017
77.2

2016
72.9


We also have certain noncancelable purchase obligations. The minimum commitment under these agreements at December 31, 2018, was $697.5 million.
The insurance operations of ARX have several multiple-layer property catastrophe reinsurance contracts with various reinsurers with terms ranging from one to three years. The minimum commitment under these contracts was $81.5 million at December 31, 2018.

Historical Timeline

Fiscal YearFiled
2018Feb 27, 2019Showing above
2017Feb 27, 2018
2016Mar 1, 2017
2015Feb 29, 2016

About Commitments Disclosures

Commitments and contingencies disclosures catalog a company's off-balance-sheet obligations and legal exposures — purchase commitments, guarantee arrangements, pending litigation, and regulatory proceedings. These items represent potential future cash outflows that may not appear as liabilities on the balance sheet until they become probable and estimable.

Key signals: litigation reserves and disclosed loss ranges quantify management's estimate of legal exposure, but unquantified "reasonably possible" losses often represent the larger risk. Watch for changes in language around pending cases — shifts from "remote" to "reasonably possible" or increases in estimated loss ranges signal deteriorating outcomes. Unconditional purchase obligations and take-or-pay contracts create fixed cost structures that reduce operational flexibility. Guarantee arrangements for subsidiaries or joint ventures can create cascading obligations. Compare the total commitment schedule against projected free cash flow to assess whether the company can meet its obligations without additional financing.