A risk-reward model with compound interest rate for non-additive two-option ski rental

We consider the non-additive two-option ski rental problem (NTSR), which includes two options such that each Option i (for i=1,2) is characterized by a one-time cost bi and a corresponding rental price ai. Without loss of generality, we assume that a1>a2≥0 and b2>b1≥0. Besides, we have to pay a transition cost c if we switch from Option 1 to Option 2, where c≥b2−b1. We introduce the compound interest rate into the continuous version of NTSR and obtain the optimal deterministic on-line strategy by competitive analysis. Moreover, considering the risk tolerance of decision makers, we present a risk-reward strategy. In addition, we use numerical analysis to analyze the influence of risk tolerance and compound interest rate on the restricted ratio and switching time of the optimal risk-reward strategy. The results demonstrate that the competitive performance is improved when the risk tolerance and compound interest rate are considered.