The on-line rental problem under risk-reward model with probabilistic forecast

Using the generalized on-line risk-reward model based on probabilistic forecasts, this paper investigates the on-line rental problem. We design the optimal reward algorithm and the minimal risk algorithm under the basic probability forecast and the geometric distribution probability forecast, respectively. In contrast to the existing competitive analysis 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/reward tolerance level and probabilistic forecast. Moreover, we also show that this model has a good linkage to the stochastic competitive ratio analysis.