The leasing industry has significant impacts on other industries, and has catalysed economic development in different countries (Peck, 2014; Vance, 2003). To decide if leasing is a profitable fi- nancing option, the decision maker should first determine the length of time the equipment will be used. However, in practice, the exact length of time for use of some equipment is usually unavailable, so researchers explore well-established techniques in the fully distribution-free model, i.e., the online model and competitive analysis (Albers, 2003; Borodin & El-Yaniv, 1998), to evaluate their strategies. This technique compares the results obtained with an online strategy to the result that could have been obtained if one had known the exact length of time in advance, with the latter scenario represented by an optimal offline strategy. Thus, the competitive analysis aims is to design an online strategy with the best possible worstcase guarantees. Competitive analysis has been used to study many problems within the fields of finance (El-Yaniv, 1998), operations research (Chen & Wang, 2015; Liu, Chu, Xu, & Zheng, 2010; Zheng, Cheng, Xu, & Liu, 2013) and management science (Larsen & Wøhlk, 2010). Karp first formulated the classic “leasing problem” (a.k.a. the Skirental problem) using the following online model and competitive analysis method (Karp, 1992): assume the decision maker has two ∗ Corresponding author. Tel.: +86 2885416013. E-mail address: ycdong@scu.edu.cn (Y. Dong). options, to lease or purchase the equipment. In the purchase option, a one-time cost is incurred, and thereafter usage is free of charge; in the lease option, the cost is proportional to usage time, and there is no one-time cost. The solution is straightforward with competitive ratio 2, i.e., the strategy never pays more than twice the optimum. There have been many generalizations of this simple problem. For example, El-Yaniv, Kaniel, and Linial (1999) incorporated interest rates into the model and determined the optimal online strategies. Irani and Ramanathan (1998) examined a situation in which the price of the equipment fluctuates while the rental cost stays constant. More recently, Lotker, Patt-Shamir, and Rawitz (2008a, 2008b) and Zhang, Ponn, and Xu (2011) proposed the multi-slope ski-rental problem and the multiple discount option ski-rental problem, respectively. Other classic variations of the problem include the replacement problem (El-Yaniv & Karp, 1997), the capital investment problem (Azar et al., 1999) and the Bahncard problem (Fleischer, 2001). The lease option in all of the above research is an operating lease. Operating leases are contracts for rent. At the end of the contract period, the ownership of the rented equipment remains with the rental company. In practice, there is another important leasing category: the financial lease. Typically, in a financial lease, the lessee will find required equipment, and then contact a leasing company (the lessor) to arrange financing. Legal ownership of the equipment remains with the lessor until lease ends, at which time the ownership is transferred to the lessee (Vance, 2003).