Abstract: Based on the on-line leasing of one kind device,the on-line device replacement problem is presented By traditional competitive ratio method,competitive strategies for the two stage device replacement problems with and without market interest rates are discussed respectively,and the risk-reward models are also provided respectively. Therofore the online person who replaces device can choose the most optimal based on their risk tolerance and forecasts. Interest rate is an essential feature of any practical online device replacement,and consideration about it is included in this paper although it made the problem more complex. Examples show that competitive ratio with interest rate is smaller,the competitive ratio decreases with interest rate;and the optimal restricted competitive ratio under risk-reward model is much smaller. Therefore,investor will take more prudent investment strategy with interest rate.

Key words: online device replacement, competitive ratio, risk-reward, interest rate