Optimal Dynamic Pricing with Demand Model Uncertainty: A Squared-Coefficient-of-Variation Rule for Learning and Earning

39 Pages Posted: 25 Nov 2014

See all articles by N. Bora Keskin

N. Bora Keskin

Duke University - Fuqua School of Business

Date Written: August 3, 2014

Abstract

We consider a price-setting firm that sells a product over a continuous time horizon. The firm is uncertain about the sensitivity of demand to price adjustments, and continuously updates its prior belief on an unobservable sensitivity parameter by observing the demand responses to prices. The firm’s objective is to minimize the infinite-horizon discounted loss, relative to a clairvoyant that knows the unobservable sensitivity parameter. Using partial differential equations theory, we characterize the optimal pricing policy, and then derive a formula for the optimal learning premium that projects the value of learning onto prices. We compare and contrast the optimal pricing policy with the myopic pricing policy, and quantify the cost of myopically neglecting to charge a learning premium in prices. We show that the optimal learning premium for a firm that looks far into the future is the squared coefficient of variation (SCV) in the firm’s posterior belief. Based on this principle, we design a simple variant of the myopic policy, namely the SCV rule, and prove that this policy is long-run average optimal.

Keywords: Dynamic pricing, revenue management, stochastic control, Bayesian learning, Gaussian prior distribution, exploration-exploitation

Suggested Citation

Keskin, N. Bora, Optimal Dynamic Pricing with Demand Model Uncertainty: A Squared-Coefficient-of-Variation Rule for Learning and Earning (August 3, 2014). Available at SSRN: https://ssrn.com/abstract=2487364 or http://dx.doi.org/10.2139/ssrn.2487364

N. Bora Keskin (Contact Author)

Duke University - Fuqua School of Business ( email )

100 Fuqua Drive
Durham, NC 27708-0120
United States

HOME PAGE: http://faculty.fuqua.duke.edu/~nk145/

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
318
Abstract Views
1,536
rank
113,311
PlumX Metrics