Mean square convergence rates for maximum quasi-likelihood estimators

Boer, AV Arnoud den; Zwart, AP Bert

doi:10.1214/12-ssy086

Cited by 5 publications

References 36 publications

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Dynamic pricing and learning: Historical origins, current research, and new directions

Boer

2015

Surveys in Operations Research and Management Science

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307

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Dynamic pricing and learning is a research topic that has received a considerable amount of attention in recent years, from different scientific communities: operations research and management science, marketing, economics, econometrics, and computer science. We survey these literature streams: we provide a brief introduction to the historical origins of quantitative research on pricing and demand estimation, point to different subfields in the area of dynamic pricing, and provide an in-depth overview of the available literature on dynamic pricing and learning. We discuss relations with methodologically related research areas, and identify several important directions for future research.

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Dynamic pricing and learning: Historical origins, current research, and new directions

Boer

2015

Surveys in Operations Research and Management Science

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307

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Chasing Demand: Learning and Earning in a Changing Environment

2017

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We consider a dynamic pricing problem in which a seller faces an unknown demand model that can change over time. We measure the amount of change over a time horizon of T periods using a quadratic variation metric, and allow a finite "budget" for such changes. We first derive a lower bound on the expected performance gap between any pricing policy and a clairvoyant who knows a priori the temporal evolution of the underlying demand model, and then design families of near-optimal pricing policies, the revenue performance of which asymptotically matches said lower bound. We also show that the seller can achieve a substantially better revenue performance in demand environments that change in "bursts" than it would in a demand environment that changes "smoothly." Finally, we extend our analysis to the case of rapidly changing demand settings, and obtain a range of results that quantify the net effect of the volatility in the demand environment on the seller's revenue performance.

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Dynamic Pricing and Learning with Finite Inventories

Boer

Zwart

2015

Operations Research

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We study a dynamic pricing problem with finite inventory and parametric uncertainty on the demand distribution. Products are sold during selling seasons of finite length, and inventory that is unsold at the end of a selling season perishes. The goal of the seller is to determine a pricing strategy that maximizes the expected revenue. Inference on the unknown parameters is made by maximum-likelihood estimation.We show that this problem satisfies an endogenous learning property, which means that the unknown parameters are learned on the fly if the chosen selling prices are sufficiently close to the optimal ones. We show that a small modification to the certainty equivalent pricing strategy-which always chooses the optimal price w.r.t. current parameter estimatessatisfies Regret T = O log 2 T , where Regret T measures the expected cumulative revenue loss w.r.t. a clairvoyant who knows the demand distribution. We complement this upper bound by showing an instance for which the regret of any pricing policy satisfies log T .

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Mean square convergence rates for maximum quasi-likelihood estimators

Cited by 5 publications

References 36 publications

Dynamic pricing and learning: Historical origins, current research, and new directions

Dynamic pricing and learning: Historical origins, current research, and new directions

Chasing Demand: Learning and Earning in a Changing Environment

Dynamic Pricing and Learning with Finite Inventories

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