We study a problem of rental rate pricing and rental contract designing in aircraft leasing industry. In a framework of Stackelberg game, the system is composed of an airline company (carrier) and an aircraft leasing company (lessor). Acting as the leader, the lessor announces daily rental rates and/or provides long-term contracts on a finite horizon with multiple periods. For each period, the carrier determines the aircraft leasing number to adjust the flight capacity, and applies a dynamic pricing policy for air-tickets based on a seasonally stochastic demand and some economic factor, such as oil price. We find the optimal policies for both lessor and carrier through a dynamic program approach.

Then, we consider a "forward-like" long-term contract in this paper. The lessor provides an identical rental rate if the carrier promises to rent a pre-determined number of aircraft on the whole horizon. Applying an appropriate long-term contract, the lessor can make more money from a large required leasing number. The carrier can improve performance from providing additional flights. Meanwhile, the customers enjoy more flight service. We are able to obtain the optimal contract design and the associated optimal policies for the entire system. In the future research, we will study more flexible contracts for the carrier and lessor to improve the profit and share the risk.