Abstract
Competitive analysis for all investors in the Bahncard problem (a railway pass of the Deutsche Bundesbahn company) has received much attention in recent years. In contrast to this common approach, which selects the riskless outcome and achieves the optimal competitive ratio, this paper introduces a risk-reward competitive strategy to achieve flexibility. Namely, we extend the traditional competitive analysis to provide a framework in which the travellers can develop optimal trading strategies based on their risk tolerance and investing capability. We further present a surprisingly flexible competitive ratio of \(r^*_A = 1 + \frac{1-\beta}{(2-\beta)t - (1-\beta)}\) for the Bahncard problem, where t is the risk tolerance and β is the percentage of discount with respect to this strategy. Then substituting t = 1 into the above equation, we obtain the (2 – β)–competitive ratio which is the best attainable result presented by Fleischer.
This research is supported by NSF of China under Grants 10371094 and 70471035.
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Ding, L., Xin, C., Chen, J. (2005). A Risk-Reward Competitive Analysis of the Bahncard Problem. In: Megiddo, N., Xu, Y., Zhu, B. (eds) Algorithmic Applications in Management. AAIM 2005. Lecture Notes in Computer Science, vol 3521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496199_6
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DOI: https://doi.org/10.1007/11496199_6
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