Integrated Risk Management for Newsvendors with Value-at-Risk Constraints

Abstract

We study a newsvendor problem with profit risk control using value-at-risk (VaR) constraints. When a firm’s demand correlates with the price of a tradable financial asset, both financial tools (derivatives) and operational tools (inventory) can be used for profit risk management. Such integrated risk management (IRM) approaches have been studied using various optimization frameworks to reflect the risk aversion of decision-makers. To the best of our knowledge, we are the first to study IRM in a newsvendor setting using profit maximization under VaR constraints. The VaR constraints allow for flexibility in the choice of profit target, [Formula: see text], and confidence level of achieving it, [Formula: see text]. It is important to understand the implications of different [Formula: see text] choices: some choices result in inventory decisions exhibiting risk aversion (and risk neutrality), whereas others result in inventory decisions exhibiting risk seeking. We demonstrate that without financial hedging, under the risk-averse [Formula: see text] choices, the decision-maker has to sacrifice mean profit for risk control by stocking below the profit-maximizing (or the risk-neutral) inventory level. When financial hedging is available, however, the decision-maker can use it alone to control the profit risk, even when demand only partially correlates with the price of the financial asset used. Thus, inventory is solely used for profit maximization, and financial hedging is solely used for profit control. This separation of inventory and financial hedging decisions simplifies the IRM implementation. Such simplification however, is not the case under the mean-variance or expected utility frameworks. In these risk-averse frameworks, both inventory and financial hedging must combine to control risk control, and, thus, these two types of decisions are often highly interdependent. VaR constraints, often preferred by regulators, may be helpful in implementing IRM in many regulated industrial settings.