Online algorithms can be used for trading financial markets such as currency conversion. We consi... more Online algorithms can be used for trading financial markets such as currency conversion. We consider a set of uni-directional non-preemptive online conversion algorithms, and investigate their performance empirically. We compute stylized facts of different datasets of the German DAX30, and estimate the ‘true’ stochastic properties of the dataset under consideration by the weighted moment method. Using the estimated parameters as input data, we generate synthetic datasets fitting an extreme value distribution. The worst-case and the empirical-case performance of known online conversion algorithms is investigated on these ‘typical datasets’. Based on the experimental data, we calculate 1) the worst-case competitive ratio cwc taking the data of the problem instance into account, and 2) the expected competitive ratio $c^{ex} = E[OPT/ON ]$ using the returns achieved by the algorithms. We report a great disparity between the worst-case and the empirical-case results, and show that the ext...
Surveys in Operations Research and Management Science, 2014
ABSTRACT This paper surveys the literature devoted to online algorithms for conversion problems. ... more ABSTRACT This paper surveys the literature devoted to online algorithms for conversion problems. We attempt to unify the terminology and the notation, while introducing the existing results based on a detailed problem classification. Algorithms on hand are reviewed based on our proposed scheme nature of search ||nature of conversion ||given information. We conclude that by the parameter given information existing algorithms as well as open problems can easily be identified.
ABSTRACT A risk measure determines the quantity of an asset that needs to be kept in reserve in o... more ABSTRACT A risk measure determines the quantity of an asset that needs to be kept in reserve in order to make the risk taken by an investor acceptable. In the last decade coherent measures of risk meeting a set of four desirable properties gain in importance.We prove the Competitive Ratio to be coherent since it satisfies the four required axioms. We explain risk management in online conversion problems, and show how the Competitive Ratio can be used to manage the risk.
This article appeared in a journal published by Elsevier. The attached copy is furnished to the a... more This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/authorsrights a b s t r a c t We answer this question using the competitive ratio as an indicator for the quality of information about the future. Analytical results show that the better the information the better the worst-case competitive ratios. However, experimental analysis gives a slightly different view. We calculate the empirical-case competitive ratios of different variants of a threat-based online algorithm. The results are based on historical data of the German Dax-30 index. We compare our experimental empirical-case results to the analytical worst-case results given in the literature. We show that better information does not always lead to a better performance in real life applications. The empirical-case competitive ratio is not always better with better information, and some a-priori information is more valuable than other for practical settings.
Online algorithms can be used for trading financial markets such as currency conversion. We consi... more Online algorithms can be used for trading financial markets such as currency conversion. We consider a set of uni-directional non-preemptive online conversion algorithms, and investigate their performance empirically. We compute stylized facts of different datasets of the German DAX30, and estimate the ‘true’ stochastic properties of the dataset under consideration by the weighted moment method. Using the estimated parameters as input data, we generate synthetic datasets fitting an extreme value distribution. The worst-case and the empirical-case performance of known online conversion algorithms is investigated on these ‘typical datasets’. Based on the experimental data, we calculate 1) the worst-case competitive ratio cwc taking the data of the problem instance into account, and 2) the expected competitive ratio $c^{ex} = E[OPT/ON ]$ using the returns achieved by the algorithms. We report a great disparity between the worst-case and the empirical-case results, and show that the ext...
Surveys in Operations Research and Management Science, 2014
ABSTRACT This paper surveys the literature devoted to online algorithms for conversion problems. ... more ABSTRACT This paper surveys the literature devoted to online algorithms for conversion problems. We attempt to unify the terminology and the notation, while introducing the existing results based on a detailed problem classification. Algorithms on hand are reviewed based on our proposed scheme nature of search ||nature of conversion ||given information. We conclude that by the parameter given information existing algorithms as well as open problems can easily be identified.
ABSTRACT A risk measure determines the quantity of an asset that needs to be kept in reserve in o... more ABSTRACT A risk measure determines the quantity of an asset that needs to be kept in reserve in order to make the risk taken by an investor acceptable. In the last decade coherent measures of risk meeting a set of four desirable properties gain in importance.We prove the Competitive Ratio to be coherent since it satisfies the four required axioms. We explain risk management in online conversion problems, and show how the Competitive Ratio can be used to manage the risk.
This article appeared in a journal published by Elsevier. The attached copy is furnished to the a... more This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/authorsrights a b s t r a c t We answer this question using the competitive ratio as an indicator for the quality of information about the future. Analytical results show that the better the information the better the worst-case competitive ratios. However, experimental analysis gives a slightly different view. We calculate the empirical-case competitive ratios of different variants of a threat-based online algorithm. The results are based on historical data of the German Dax-30 index. We compare our experimental empirical-case results to the analytical worst-case results given in the literature. We show that better information does not always lead to a better performance in real life applications. The empirical-case competitive ratio is not always better with better information, and some a-priori information is more valuable than other for practical settings.
Uploads