Arnoud V. Den Boer

University of Amsterdam | UVA · Institute of Mathematics Korteweg-De Vries

A key step in data-driven decision making is the choice of a suitable mathematical model. Complex models that give an accurate description of reality may depend on many parameters that are difficult to estimate; in addition, the optimization problem corresponding to such models may be computationally intractable and only approximately solvable. Sim...

The topic of dynamic pricing and learning has received a considerable amount of attention in recent years, from different scientific communities. 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...

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 t...

We study the behavior of maximum quasi-likelihood estimators (MQLEs) for a class of statistical models, in which only knowledge about the first two moments of the response variable is assumed. This class includes, but is not restricted to, generalized linear models with general link function. Because the MQLE may not always exist, we consider the l...

Price experimentation is an important tool for firms to find the optimal selling price of their products. It should be conducted properly, since experimenting with selling prices can be costly. A firm, therefore, needs to find a pricing policy that optimally balances between learning the optimal price and gaining revenue. In this paper, we propose...

We consider dynamic pricing and demand learning in a duopoly with multinomial logit demand, both from the perspective where firms compete against each other and from the perspective where firms aim to collude to increase revenues. We show that joint‐revenue maximization is not always beneficial to both firms compared to the Nash equilibrium, and sh...

We consider a seller’s dynamic pricing problem with demand learning and reference effects. We first study the case in which customers are loss-averse: they have a reference price that can vary over time, and the demand reduction when the selling price exceeds the reference price dominates the demand increase when the selling price falls behind the...

We consider dynamic assortment optimization with incomplete information under the uncapacitated multinomial logit choice model. We propose an anytime stochastic approximation policy and prove that the regret—the cumulative expected revenue loss caused by offering suboptimal assortments—after T$$ T $$ time periods is bounded by T$$ \sqrt{T} $$ times...

We consider price optimization under the finite-mixture logit model. This model assumes that customers belong to one of a number of customer segments, where each customer segment chooses according to a multinomial logit model with segment-specific parameters. We reformulate the corresponding price optimization problem and develop a novel characteri...

Problem definition: This paper addresses the question whether or not self-learning algorithms can learn to collude instead of compete against each other, without violating existing competition law. Academic/practical relevance: This question is practically relevant (and hotly debated) for competition regulators, and academically relevant in the are...

This paper considers a novel formulation of the classical assortment optimization problem with multinomial logit demand and unknown model parameters. The novelty lies in the fact that the set of products is not finite but a continuum, motivated by the desire to understand the problem characteristics for many products, as well as by applications whe...

In this note, we consider dynamic assortment optimization with incomplete information under the capacitated multinomial logit choice model. Recently, it has been shown that the regret (the cumulative expected revenue loss caused by offering suboptimal assortments) that any decision policy endures is bounded from below by a constant times $\sqrt {NT...

We study price optimization of perishable inventory over multiple, consecutive selling seasons in the presence of demand uncertainty. Each selling season consists of a finite number of discrete time periods, and demand per time period is Bernoulli distributed with price-dependent parameter. The set of feasible prices is finite, and the expected dem...

A key step in data-driven decision making is the choice of a suitable mathematical model. Complex models that give an accurate description of reality may depend on many parameters that are difficult to estimate; in addition, the optimization problem corresponding to such models may be computationally intractable and only approximately solvable. Sim...

We consider a dynamic pricing problem with an unknown and discontinuous demand function. There is a seller who dynamically sets the price of a product over a multiperiod time horizon. The expected demand for the product is a piecewise continuous and parametric function of the charged price, allowing for possibly multiple discontinuity points. The s...

This paper presents the results of the Dynamic Pricing Challenge, held on the occasion of the 17th INFORMS Revenue Management and Pricing Section Conference on June 29-30, 2017 in Amsterdam, The Netherlands. For this challenge, participants submitted algorithms for pricing and demand learning of which the numerical performance was analyzed in simul...

We consider assortment optimization in relation to a product for which a particular attribute can be continuously adjusted. Examples include the duration of a loan (where each duration corresponds to a specific interest rate) and the data limit for a cell phone subscription. The question to be addressed is: how should a retailer determine what to o...

We study a single-product fluid-inventory model in which the procurement price of the product fluctuates according to a continuous time Markov chain. We assume that a fixed order price, in addition to state-dependent holding costs are incurred, and that the depletion rate of inventory is determined by the sell price of the product. Hence, at any ti...

This paper explores the boundary of the set of reaction networks that have an exact transient (truncated) multidimensional Poisson or product-form distribution for the number of particles of different types. Motivated by the birth–death process, we introduce the notions of transient detailed balance and delay functions, and use these notions to obt...

Dynamic pricing of commodities without knowing the exact relation between price and demand is a much-studied problem. Most existing studies assume that the parameters describing the market are constant during the selling period. This severely reduces their practical applicability, since, in reality, market characteristics may change all the time, w...

In this note we study the behavior of maximum quasilikelihood estimators (MQLEs) for a class of statistical models, in which only knowledge about the first two moments of the response variable is assumed. This class includes, but is not restricted to, generalized linear models with general link function. Our main results are related to guarantees o...

This paper considers the problem of estimating probabilities of the form $\mathbb{P}(Y \leq w)$, for a given value of $w$, in the situation that a sample of i.i.d.\ observations $X_1, \ldots, X_n$ of $X$ is available, and where we explicitly know a functional relation between the Laplace transforms of the non-negative random variables $X$ and $Y$....

We study a dynamic pricing problem with multiple products and infinite inventories. The demand for these products depends on the selling prices and on parameters unknown to the seller. Their value can be learned from accumulating sales data using statistical estimation techniques. The quality of the parameter estimates is influenced by the amount o...

Intuitively one might expect that the quality of statistical estimates cannot worsen if they are based on more data. We show in a least-squares linear regression setting that this intuition is wrong. Adding data may worsen the quality of parameter estimates, and in fact may even cause a design sequence to lose strong consistency.

For a seller operating in a nonstationary demand setting, a key question is how to collect and filter data to find the optimal prices for its products. In this chapter, we discuss the commonly used frameworks for dynamic pricing and demand learning in nonstationary demand settings. For exogenously changing demand settings, we provide an overview of...

Determining the right price is a fundamental business problem that can be addressed by data-driven methods. In this chapter, we discuss several pricing policies that learn the optimal price from accumulating sales data, both in parametric and nonparametric models, and both for single-product and multiple product settings. We also discuss possible f...

Harvey Friedman introduced natural independence results for the Peano axioms (PA) via certain schemes of combinatorial well-foundedness. We consider in this article parameterized versions of a specific Friedman-style scheme and classify exactly the threshold for the transition from provability to unprovability in PA. For this purpose we fix a natur...