A utility adjusted newsvendor model with stochastic demand

We develop a continuous time Newsvendor model to determine the optimal inventory level for commodities in an established financial market. Unlike most models in literature, the newsvendor is not necessarily risk-neutral and chooses the order quantity that maximises the expected utility of the cash flow at the end of the period. The newsvendor exploits the correlation between stochastic demand and the price of the commodities, in order to manage risks by investing in a portfolio of financial instruments. The decision problem, therefore, includes not only the determination of the optimal ordering policy, but also, at the same time, the selection of a portfolio that maximises her utility. Further, we demonstrate that our model, compared to a myopic approach (i.e. no hedging), requires significantly lower levels of inventory buffer to mitigate demand uncertainty, thus better utilising capital.