价格呈几何布朗运动规律的出口海陆仓质押率优化

针对质押物价格呈几何布朗运动规律、与需求呈线性下降关系下的出口海陆仓融资质押率优化问题,利用条件概率原理,分析获得了出口海陆仓融资各种情形发生概率,通过同时考虑质押物陆上仓储费用和海上运输费用,构建了船公司融资(期望)利润分段函数模型,并运用数值逼近法和解析法设计了最优质押率的求解算法步骤.算例验证了模型和算法的适用性和有效性.敏感性分析结果表明最优质押率与质押物价格呈负相关关系,与质押量呈正相关关系;船公司最大期望利润与质押物价格呈正相关关系,随着质押量的增加,船公司最大期望利润呈先上升后下降趋势.研究结论可为船公司制定融资优化决策提供科学的参考.

Optimization on loan-to-value ratios of exporting offshore/in-transit inventory financing with geometric Brownian motion process price

This paper addressed the issue of loan-to-value ratios optimization on exporting offshore/in-transit inventory financing under the condition that the collateral price follows geometric Brownian motion process and shows a liner negative correlation with demand. Firstly, the probabilities of the events occurred in the exporting offshore/in-transit inventory financing were figured out through the analysis of conditional probability. After that, the piecewise function model of the shipping company's financing (expected) profit was established concerning both the land storage costs and ocean freights. Finally, this paper gave the optimization solution steps of the algorithm by using the numerical approximation method and analytical method. Numerical example verified the applicability and validity of the proposed model and algorithm. The results of sensitivity analysis show that the optimal loan-to-value ratio has a negative correlation with the price of collaterals and a positive correlation with the volume of collaterals, respectively; the maximum expected profit of the shipping company has a positive correlation with the price of collaterals. An additional finding is that the maximum expected profit of the shipping company rises firstly and then declines with the increasing of the volume of collaterals. The findings of this paper can provide a scientific reference for the shipping company in financing optimization decisions.