Abstract: Exporting offshore/in-transit inventory financing means that the bank regards the shipping company's credit guarantee as a condition, and commissions the shipping company to supervise and transport pledged goods throughout the entire journey (offshore warehouse, in transit, to the destination warehouse). It's a new inventory mortgaging/financing mode with worldwide credit, which can not only relieve exporters in terms of a shortage of funds, but can also bring new types of profit growth points for banks and shipping companies. Exporting offshore/in-transit inventory financing has practical significance for promoting the development of seaborne trade and supply chain finance. The optimization of its loan-to-value ratio, namely the ratio of loan principal and the value of the pledged goods, is the key to manage and control the risk.
According to the process of exporting offshore/in-transit inventory financing,the trading decisions of the shipping company, exporter and importer reflect the relationship of a double Stackelberg Game strategy. The first game occurs between the shipping company and exporter. The shipping company sets the loan-to-value ratio r first, and then the exporter determines the delivery lead time L accordingly. Therefore, the shipping company is the leader, and the exporter is the follower in the game. The second game takes place between the exporter and the importer. The exporter sets the delivery lead time L first, and then the importer determines the order quantities Q accordingly. Therefore, the exporter is the leader and the importer is the follower in the game. In international seaborne trade, demand fluctuations will affect the value of pledged goods, which may result in non-compliance. When the market price of the pledged goods is higher than the purchase price signed by the importer and exporter, the importer will withdraw the pledged goods normally. Otherwise, the importer and exporter are likely to default, so the shipping company could sell the collateral to make up the loan capital.
In this paper, the issue of optimization on loan-to-value ratios of exporting offshore/in-transit inventory financing under uncertain demand is addressed. Based on the theory of double Stackelberg game, the total profit functions under four game strategies among the shipping company, exporter and importer are analyzed and constructed, aiming at maximizing the total profit of the supply chain. The piecewise function optimization model of loan-to-value ratios is established. The existence of optimal loan-to-value ratios is proved. A reverse reasoning method is adopted to solve the model. The solution process is designed as follows:firstly, maximize the profit of the exporter to get the expression of the best delivery lead time L^* containing r, secondly, maximize the profit of the importer to get the expression of the economic ordering quantity Q^* containing L^*, then the optimal loan-to-value ratio r^* is solved by maximizing the total profit function.
Numerical example is used to verify the applicability and validity of the proposed model. The results indicate that the optimal loan-to-value ratio has a positive correlation with the importer's purchase price, and has a negative correlation with the market price and raw material price of pledged goods, respectively. Therefore, the shipping company should keep a close eye on the price changes of pledged goods, and set a reasonable loan-to-value ratio to increase the total profits of the supply chain. The findings can provide scientific guidance for the optimization of exporting offshore/in-transit inventory financing.

Key words: exporting offshore/in-transit inventory, financing, loan-to-value ratio, double Stackelberg Games, reverse reasoning method