Abstract: In real rental market, based on the fact that the rental cost and purchase price of an equipment generally continue to rise as time goes, we put forward the on-line strategy for the rental problem both with the interest rate and the increasing price index, and also propose the risk-reward model based on probabilistic forecasts. Firstly, by using the method of on-line algorithm and competitive analysis, we design the optimal investment strategy and competitive ratio for this problem. Then, under the risk-reward framework, we discuss the maximum reward strategy based on the given risk tolerance and the future forecast. More, we propose another risk model for this problem which can obtain the minimum risk strategy under the given reward level and the future forecast. Finally, the optimal competitive performance of the strategy is discussed and illustrated by numerical analysis, which shows that the competitive performance of on-line strategy increases significantly in the risk-reward models with probabilistic forecast.

Key words: on-line leasing problem, risk-reward, competitive analysis, inflation, interest rate

摘要： 考虑到实际租赁市场中设备的租赁和购买价格随着时间推移持续上涨的特征,研究了通货膨胀市场中的租赁问题在有利率情形下的在线竞争策略,并建立了相应的概率预期的风险补偿模型。首先运用在线算法和竞争分析理论设计了该问题的最优竞争策略,并给出最优竞争比。接着,在风险补偿竞争分析框架下,进一步讨论该问题,投资者可以控制风险,根据自己不同的风险容忍度和未来预期选择补偿最大的租赁策略;也可以根据给定的补偿收益约束选择风险最小的策略。最后通过数值分析,验证了相关结论的正确性,也表明了基于概率预期的风险补偿策略大大改善了该租赁问题的竞争比性能。

关键词: 在线租赁问题, 风险补偿, 竞争分析, 通货膨胀, 市场利率