We study dynamic operational decision problems where risky cash flows are being resolved over a finite planning horizon. Financing decisions via lending and borrowing are available to smooth out consumptions over time with the goal of achieving some prescribed consumption targets. Our target-oriented decision criterion is based on the aggregation of Aumann and Serrano (2008) riskiness indices of the consumption excesses over targets, which has salient properties of subadditivity, convexity and respecting second-order stochastic dominance. We show that if borrowing and lending are unrestricted, the optimal policy of this criterion is to finance consumptions at the target levels for all periods except the last. Moreover, the optimal policy has the same control state as the optimal risk neutral policy and could be achieved with relatively modest computational effort. Under restricted financing, we show that for convex dynamic decision problems, the optimal policies correspond to those that maximize expected additive-exponential utilities, and can be obtained by an efficient algorithm. We also analyze the optimal policies of joint inventory-pricing decision problems under the target-oriented criterion and provide optimal policy structures. With a numerical study for inventory control problems, we report favorable computational results for using targets in regulating uncertain consumptions over time.
Citation
Working paper, NUS Business School and NUS Risk Management Institute, September/2011