Online (J,K)(J,K)-search problem and its competitive analysis

This work proposes an online (J,K)(J,K)-search problem where an online player has K   units of some asset for selling and has to sell at least J≤KJ≤K units of the asset in a finite number of periods. At the beginning of each period a quoted price is observed and the player has to decide immediately and irrecoverably whether to accept the price as well as the amount of the asset to be sold at the price. The objective is to maximize average selling price. We present two models where at most one unit of the asset can be sold in each period and where one or more units of the asset can be sold in each period. For both models we propose optimal online deterministic algorithms.