Commitments and Contingencies

(a) We purchase annuities from life insurance companies to fulfill obligations under claim settlements that provide for periodic future payments to claimants. As of December 31, 2017, we had purchased such annuities with a present value of $18.5 million for settlement of claims on a structured basis for which we are contingently liable. To our knowledge, there are no material defaults from any of the issuers of such annuities.

(b) We have various operating leases for office space, equipment, and fleet vehicles. Such lease agreements, which expire at various times, are generally renewed or replaced by similar leases. Rental expense under these leases amounted to $10.8 million in 2017, $12.3 million in 2016, and $11.7 million in 2015. We also lease computer hardware and software under capital lease agreements expiring at various dates through 2019. See item (p) of Note 2. "Summary of Significant Accounting Policies" in this Form 10-K for information on our accounting policy regarding leases.

In addition, certain of these leases are non-cancelable, and liability for payment will continue even though the leased asset may no longer be in use. At December 31, 2017, the total future minimum rental commitments under non-cancelable leases were as follows:



($ in millions)	Capital Leases		Operating Leases	Total
2018	$	2.3	10.0	12.3
2019	0.1		7.5	7.6
2020	—		6.0	6.0
2021	—		3.7	3.7
2022	—		2.1	2.1
After 2022	—		2.6	2.6
Total minimum payment required	$	2.4	31.9	34.3

(c) As of December 31, 2017, we had contractual obligations that expire at various dates through 2032 to invest up to an additional $221 million in alternative and other investments. There is no certainty that any such additional investment will be required. For additional information regarding these investments, see item (f) of Note 5. "Investments" in this Form 10-K. In addition, as of December 31, 2017, we had contractual obligations that expire in 2023 to invest $16.3 million in a non-publicly traded common stock within our available-for-sale portfolio. We expect to have the capacity to repay and/or refinance these obligations as they become due.