American Institute of Mathematical Sciences

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January  2010, 6(1): 1-14. doi: 10.3934/jimo.2010.6.1

Competitive risk management for online Bahncard problem

Lili Ding 1, , Xinmin Liu 1, and  Yinfeng Xu 2,

1. 

Economics and Management College, Shandong University of Science and Technology, Qingdao, China, China
2. 

School of Management, Xi’an Jiaotong University, Xi’an, China

Received  July 2008 Revised  June 2009 Published  November 2009

In the Bahncard problem a traveler decides when to buy a Bahncard, i.e., a railway discount card of the German Deutsche Bundesbahn company, in an online setting. This problem is introduced by Fleischer and some optimal deterministic algorithms are presented with a fixed Bahncard price. In practice, however, travelers are trying to manage their risks by using some forms of rewards and their forecasting skills. We extend Fleischer's model to a new one in a risk management framework. For such an extended problem, we provide some flexible results which can be used by a traveler to obtain an optimal risk algorithm based on his risk tolerance and forecast. We further study another extention of the Bahncard problem with a fluctuated Bahncard price. We propose some algorithms and analyze their competitive ratios with and without risk, respectively. It turns out that a traveler can significantly improve his risk management performance by putting reasonable forecasts in conventional competitive analysis.
Keywords: online algorithm., Risk management, competitive analysis.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Lili Ding, Xinmin Liu, Yinfeng Xu. Competitive risk management for online Bahncard problem. Journal of Industrial & Management Optimization, 2010, 6 (1) : 1-14. doi: 10.3934/jimo.2010.6.1
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