Monotone trends in inventory-price control under time-consistent coherent risk measure

We use the concept of time-consistent coherent risk measure to study a risk-averse firm's inventory and price control activities. Structural characterization for an optimal inventory policy reminiscent of the risk-neutral counterpart is easy to achieve. More interestingly, monotone properties can be derived for the pricing policy when the risk possesses certain order-theoretic structures. We also introduce the concept of optimism. Two risk measures thus ranked produce inventory and pricing decisions that can be ranked themselves. The involved coherent risk measure can be a mixture of the ordinary expectation and the conditional value at risk.