Capital constraint, immensely existing in practice, became major stressors for manufacturers during the green research and development (R & D) triggered by managers integrating green concept into their business models. Considering the initial capital of a capital-constrained manufacturer, this paper formulates a Stackelberg game model comprising a manufacturer and a retailer, to discuss the optimal operation and financing decisions under the bank financing channel and trade credit financing channel, to detect the relationship between the manufacturer’s initial capital and green R & D investment, and to find which financing channel is better by comparing the two financing channels when the same initial capital is set. According to the above analysis, the results find that the capital-constrained manufacturer prefers financing only when meeting certain conditions. Furthermore, financing might be detrimental to the manufacturer but always beneficial to the retailer. Especially, under trade credit financing channel, the profit improvement of the retailer is higher than the manufacturer in the same financing channel, which suggests that the retailer has strong internal motivation to cooperate with the manufacturer from the perspective of financing.

This study proposes an exotic option that extends the classical European option by requiring option holders to continuously trade in underlying assets according to a predesignated trading strategy with a general logarithmic position. The pricing formula for the exotic option with a general logarithmic strategy is derived from the Black–Scholes option pricing formula, and its price advantage is compared (based on simulations) to the classical European option and to the exotic option with a linear position. By varying key parameters, we found that the exotic option with a general logarithmic position has a significant price advantage (up to 34% under certain parameter settings) over the classical European option. Moreover, the exotic option with a general logarithmic strategy can save 5.5% more of the option premium than applying a linear position strategy. Our simulation results indicate that the price advantage of this proactive hedging option with a general logarithmic strategy depends heavily on the initial amount of capital; in particular, this exotic option is more suitable for traders with limited initial amounts of capital.

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