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Abstract
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.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
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