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. The model calls for worst-case analysis over a convex set of demand-distribution scenarios in every period. Structural characterization for an optimal inventory policy reminiscent of the risk-neutral counterpart is easy to achieve. More interestingly, mild monotone properties can be derived for the pricing policy when the convex risk set constitutes a lattice under a suitably defined partial order. We also introduce the concept of optimism using the strong set order between risk sets. Two risk measures thus ranked produce inventory and pricing decisions that can be ranked themselves.