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A Price Hedging Model in Dynamic Market | Science Publications

机译：动态市场中的价格对冲模型科学出版物

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> Problem statement: Pricing is a problem when a firm has to set a price for the first time. This happens when the firm develops or acquires a new product, introduces its regular product into a new distribution or geographical area, or enters bids on the new contract work. Many companies try to set the price to maximize current profits. They estimate the demand and costs associated with alternative prices and choose the price that maximizes current profit, cash flow, or rate of return on investment. There are, however, some problems associated with the current profit maximizing approach as it assumes that the firm knows its demand and cost functions; in reality, demand is difficult to estimate and is unpredictable. Approach: Due to demand?s unpredictability, we assume that it follows a lognormal random walk. Based on this, we develop a mathematical pricing processes model by stochastic calculus, which is similar to the financial process mathematical model. From Ito?s lemma, a product?s profit correlates with demand, is also unpredictable and follows a random walk. Such random behavior is the marketing risk. Results: By choosing a price strategy to eliminate randomness, called price hedging, we obtain risk-free profit determined by the Black-Scholes equation. This riskless profit, which is predictable, is the same we would get by putting the equivalent amount of cash in a risk-free interest-bearing account. Conclusion: From price hedging and the Black-Scholes equation, we determine the basic product price, which changes with time and demand.
机译： > 问题陈述：当企业必须首次设定价格时，定价是一个问题。当公司开发或购买新产品，将其常规产品引入新的分销或地理区域或为新的合同工作进行投标时，就会发生这种情况。许多公司试图设定价格以使当前利润最大化。他们估计与替代价格相关的需求和成本，并选择使当前利润，现金流量或投资回报率最大化的价格。但是，当前的利润最大化方法存在一些问题，因为它假设公司知道其需求和成本函数;在现实中，需求难以估计且不可预测。方法：由于需求的不可预测性，我们假设需求遵循对数正态随机游动。在此基础上，我们通过随机演算建立了一个数学定价过程模型，该模型类似于金融过程数学模型。从伊藤引理出发，产品的利润与需求相关，也是不可预测的，并且是随机游走的。这种随机行为是营销风险。 结果：通过选择一种消除随机性的价格策略（称为价格套期保值），我们可以获得由 Black-Scholes 公式确定的无风险利润。这种无风险的利润是可以预见的，这与我们将等量的现金放入无风险的计息账户中的情况相同。 结论：通过价格套期保值和Black-Scholes方程，我们确定了基本产品价格，该价格随时间和需求而变化。

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