Inventory and Price Control under Time-consistent Coherent and Markov Risk Measure–Unabridged Version

We use the recently proposed concept of time-consistent coherent and Markov risk measure on the study of a risk-averse firm’s inventory and price control activities. In our shock-driven setting which is different from the state-driven setting where the measure is first introduced, we show the suitability of dynamic programming formulations. On this basis, we examine pure inventory and joint inventory-price control problems. The resulting model calls for worst-case analysis over a convex set of demand-distribution scenarios in every period. We achieve structural characterizations for optimal policies that are reminiscent of their risk-neutral counterparts. Monotone properties are 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.