# American Institute of Mathematical Sciences

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

## Competitive risk management for online Bahncard problem

 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.
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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