Problem Definition: We investigate a seller's optimal advertising campaign strategy targeting customers who interact with the seller over time. We model customers' engagement as a continuous-time Markov chain with two states, active and inactive. While in the active state, customers make purchases according to a Poisson process, with each purchase yielding a specific reward; in contrast, customers in the inactive state make no purchases. The seller aims to optimize the expected average profit by promptly activating customers through costly advertising campaigns contingent on their purchase histories.

Methodology/Results: For the unconstrained problem, we demonstrate the optimality of a threshold policy based on the elapsed time since the last purchase or ad campaign. When confronted with a budget constraint on the overall ad cost, we suggest first solving a static problem and then implementing a separate threshold policy for each customer with a specified budget. We establish the asymptotic optimality of this policy and show that the asymptotic loss order is $O(1/\sqrt{T})$. Furthermore, we explore two extensions: strategic customer reactions and probabilistic customer activation. Despite these additional complexities, our main findings remain robust, yielding additional insights into these scenarios.

Managerial Implication: Our findings reveal that the seller tends to push ads earlier to customers with high purchase rates and low recapture rates (i.e., low transition rates from an inactive state to an active state). Surprisingly, we also observe that the seller should push ads earlier to customers with intermediate churn rates (i.e., intermediate transition rates from an active state to an inactive state) compared to those with small or large churn rates. Moreover, we propose an easy-to-implement and asymptotically optimal policy under budget constraints.

Government regulations on emission control can be broadly divided into two categories: price instruments and quantity instruments. In this paper, we develop a stylized model to compare the two instruments in the presence of market uncertainty. We find that when the emission intensity (i.e., emissions per unit of production) and the market uncertainty are both high or low, the expected social welfare under the price instruments will be higher; otherwise, the performance of the quantity instruments is comparatively better. The results are robust when incorporating firm competition and national/regional pollution damage.  Afterward, we demonstrate that the government's quick-response capability or a hybrid of the price and quantity instruments can improve the expected social welfare, especially for high-emitting industries when the market uncertainty is intermediate. Lastly, for heterogeneous firms, we find that allowing permit trading in the quantity instrument may not be beneficial when pollution from each firm is more likely to have regional effects.

Problem Definition: We consider two business models for a two-sided economy under uncertainty: dealership and marketplace with fulfillment services. Although both business models can bridge the gap between demand and supply, it is not clear which model is better for the firm or for the consumers. Methodology/Results: We show that while the two models differ substantially in pricing power, inventory risk, fee structure, and fulfillment time, both models share several important features, with the revenues earned by the firm from the two models converging when the markets are thick. We also show that for thick markets there is a one-to-one mapping between their corresponding optimal policies. Managerial implications: Our results provide guidelines for firms entering two-sided markets: when the market is thick, the two business models are similar; when the market is thin, they should carefully inspect a number of market conditions before making the choice.