Mathematical Pricing Model in Dynamic Market with Demand Uncertainty

摘要

The price determination of goods and services in marketing management has become an important topic in the literature. We propose a pricing model in a monopolist market with demand uncertainty. The mathematics of the model assumes that the probability distribution of the market demand is given by the lognormal distribution, and develops a stochastic model to describe the random process of pricing. From Ito's calculus, the profit of goods and services is correlated with demand uncertainty and follows a lognormal random process. This random process of the market demand is the source of the risk in marketing goods and services. A price hedging strategy is applied to eliminate the randomness in the model. From the Black-Scholes equation, we can show the time behavior of the profits and prices of products.