A Risk-Reward Competitive Analysis of the Bahncard Problem

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...

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Bibliographic Details
Published inAlgorithmic Applications in Management pp. 37 - 45
Main Authors Ding, Lili, Xin, Chunlin, Chen, Jian
Format Book Chapter Conference Proceeding
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg 2005
Springer
SeriesLecture Notes in Computer Science
Subjects
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
Mathematical programming
Operational research and scientific management
Operational research. Management science
Theoretical computing
Railway
Discount
Algorithmics
Tolerance
Rail vehicle
Risk analysis
Flexibility
Modeling
Mediation
Optimal strategy
Rail transportation
Reward
Mathematical programming
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ISBN3540262245
9783540262244
ISSN0302-9743
1611-3349
DOI10.1007/11496199_6

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Summary: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.
Bibliography:This research is supported by NSF of China under Grants 10371094 and 70471035.
Original 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$r^*_A = 1 + \frac{1-\beta}{(2-\beta)t - (1-\beta)}$\end{document} 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.
ISBN:3540262245
9783540262244
ISSN:0302-9743
1611-3349
DOI:10.1007/11496199_6