购价租金降低下赁购平衡在线策略的最优性分析

证明了在购价与租金随时间降低，且决策时间未定的情况下，获得具有上界为2的最小竞争比的近似最优在线策略，即仅当实时购买价格与已累积租金额的数量关系为相等时选择购买。该研究分别针对购价租金恒定与一般情形两种情况下，不同的市场崩溃时间与设备购买时间的先后关系、购买价格与累计租金的数量关系进行了分析论证，为赁购平衡策略在现实租买决策中的应用提供了理论依据。

Optimality analysis of renting-buying balance online strategy for decrease of price and rent

We prove that buying strategy should be applied only if real time price equals to accumulated rent amount to obtain approximately optimal online strategy with the smallest competitive ratio whose upper bound is 2 under the decrease of purchase price and rent with time and indefinite decision time.We analyze serial relationship between different market crushing time and equipment buying time and quantitative relationship between purchase price and accumulated rent for such two cases as constant price and rent and general situation. Our conclusion will provide a theoretical reference for the application of renting buying balance strategy in practical rent-buy decision.