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, when it introduces its regular product into a new distribution or geographical area, and when it enters bids on new contract work. Many companies try to set the price that will maximize current profits. They estimate the demand and costs associated with alternative prices and choose the price that produces maximum current profit, cash flow, or rate of return on investment.There are some problems associated with current profit maximization. It assumes that the firm has knowledge of its demand and cost functions; in reality, the demand is difficult to estimate and unpredictable. Due to its unpredictability, we assume that the demand follows a lognormal random walk. We then develop a mathematical modeling of pricing processes by stochastic calculus, which is just like the mathematical modeling of financial processes. From Ito’s lemma, the profit of a product has a correlation with the demand, is also unpredictable and follows a random walk. Such a random behavior is the risk of marketing. By choosing a price strategy to eliminate the randomness, which is called price hedging, we obtain a risk-free profit determined by the Black-Scholes equation. This riskless profit, which is predictable, is the same as the growth we get if we put the equivalent amount of cash in a risk-free interest-bearing account.
