Integrated Capacity and Exchange Rate Hedging in Multi-Markets under Value-at-Risk

We consider the optimal integrated capacity and financial hedging strategies for a downside risk-averse global firm that faces multiple demand and foreign exchange rate risks. The firm maximizes the expected profit while controlling its profit-risk through a Value-at-Risk (VaR) constraint, which ensures the probability of the realized profit below a profit reservation level is within tolerance. A breakthrough of our research is to identify a tractable approach to resolving the well-known challenging VaR constraint. This approach allows us to consider multiple foreign markets instead of only a single foreign market under other risk measures typically assumed in the literature. We characterize efficient financial hedging under any given capacity in a general form that can be replicated with vanilla derivatives, making the profit reservation level and tolerance level interchangeable. Using this fact, we show that the optimal capacity is either the risk-neutral solution or on the boundary of the feasible region, in contrast to the mean-variance framework where multiple solutions may occur for multi-markets. We demonstrate that operational and financial hedging can be either substitutes or complements, depending on the hedging scenario