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, 2018, we had purchased such annuities with a present value of $21.0 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 $10.4 million in 2018, $10.8 million in 2017, and $12.3 million in 2016. We also lease computer hardware and software under capital lease agreements expiring at various dates through 2022. 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, 2018, the total future minimum rental commitments under non-cancelable leases were as follows:



($ in millions)	Capital Leases		Operating Leases	Total
2019	$	0.7	7.8	8.5
2020	0.1		7.4	7.5
2021	—		5.1	5.1
2022	—		3.6	3.6
2023	—		2.9	2.9
After 2023	—		9.7	9.7
Total minimum payment required	$	0.8	36.5	37.3

(c) As of December 31, 2018, we had contractual obligations that expire at various dates through 2036 to invest up to an additional $202.3 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, 2018, we had the following contractual obligations: (i) $17.8 million to further invest in non-publicly traded common stock within our equity portfolio that expire in 2023; and (ii) $40.4 million to further invest in non-publicly traded CLOs in our fixed income securities portfolio that expire through 2030. We expect to have the capacity to repay and/or refinance these obligations as they become due.