Robust pricing with asymmetric distributional information in valuation

We study a distributionally robust pricing model aimed at maximizing the worst-case profit under limited knowledge of consumers’ valuation distribution. In addition to mean and variance, we incorporate asymmetric distributional information through semivariance, and then explore the robust optimal posted and randomized pricing strategy. We obtain the robust posted price and show that several series of asymptotic three-point distributions can approach the worst case gradually. The inclusion of asymmetry enables sellers to design three distinct pricing strategies, each corresponding to a different level of asymmetry with explicitly defined thresholds. For the randomized pricing problem, we derive a near-optimal strategy by identifying three key pricing candidates. To avoid the complexity of implementing the optimal randomized price, we also explore a compromise strategy that employs a finite set of pricing candidates, which we formulate as a second-order cone program. Furthermore, we provide numerical evidence highlighting the advantages of incorporating asymmetric distributional information over the mean–variance approach, from both the worst-case profit and actual profit perspectives. Our numerical experiments also reveal that posted pricing is more effective for low-cost products, while randomized pricing is preferable for higher-cost items.