Technical Note—Price Trends in a Dynamic Pricing Model with Heterogeneous Customers: A Martingale Perspective

Abstract

This note describes probabilistic properties of optimal price sample paths in a dynamic pricing model with a finite horizon and limited stock. We assume that customer arrivals follow a nonhomogeneous Poisson process. We show that if customers' willingness-to-pay increases rapidly over time, then the optimal price process follows a submartingale, which implies an upward price trend. Alternatively, if customers' willingness-to-pay decreases rapidly over time, then the optimal price process follows a supermartingale, which implies a downward price trend.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 29 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.