Dynamic pricing in retail with diffusion process demand

TL;DR

This paper models demand randomness in retail pricing using diffusion processes within a stochastic control framework, providing a scalable approach that captures demand volatility and offers insights into near-optimal pricing policies.

Contribution

It introduces a diffusion process-based model for demand in dynamic pricing, improving scalability and demand volatility modeling over traditional Poisson-based models.

Findings

Deterministic pricing policy is nearly optimal under demand uncertainty.

Closed-form solutions are derived for the no-randomness case.

Numerical errors can lead to lower profits than heuristic policies.

Abstract

When randomness in demand affects the sales of a product, retailers use dynamic pricing strategies to maximize their profits. In this article, we formulate the pricing problem as a continuous-time stochastic optimal control problem and find the optimal policy by solving the associated Hamilton-Jacobi-Bellman (HJB) equation. We propose a new approach to modelling the randomness in the dynamics of sales based on diffusion processes. The model assumes a continuum approximation to the stock levels of the retailer which should scale much better to large-inventory problems than the existing Poisson process models in the revenue management literature. The diffusion process approach also enables modelling of the demand volatility, whereas Poisson process models do not. We present closed-form solutions to the HJB equation when there is no randomness in the system. It turns out that the deterministic pricing policy is near-optimal for systems with demand uncertainty. Numerical errors in calculating the optimal pricing policy may, in fact, result in a lower profit on average than with the heuristic pricing policy.