A risk-reward competitive analysis of the bahncard problem

  • Authors:

  • Lili Ding;Chunlin Xin;Jian Chen

  • Affiliations:

  • School of Management, Xi'an Jiaotong University, Shaanxi, P.R. China;School of Management, Xi'an Jiaotong University, Shaanxi, P.R. China;School of Management, Xi'an Jiaotong University, Shaanxi, P.R. China

  • Venue:
  • AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
  • Year:
  • 2005

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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.