Abstract
This paper proposes a generalized on-line risk-reward model, by introducing the notion of the probabilistic forecast. Using this model, we investigate the on-line rental problem. We design the risk rental algorithms under the basic probability forecast and the geometric distribution probability forecast, respectively. In contrast to the existing competitive analyses of the on-line rental problem, our results are more flexible and can help the investor choosing the optimal algorithm according to his/her own risk tolerance level and probabilistic forecast. Moreover, we also show that this model has a good linkage to the stochastic competitive ratio analysis.
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