اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDynamic Pricing and Learning under the Bass Model
65
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider a novel formulation of the dynamic pricing and demand learning problem, where the evolution of demand in response to posted prices is governed by a stochastic variant of the popular Bass model with parameters $alpha, beta$ that are linked to the so-called innovation and imitation effects. Unlike the more commonly used i.i.d. and contextual demand models, in this model the posted price not only affects the demand and the revenue in the current round but also the future evolution of demand, and hence the fraction of potential market size $m$ that can be ultimately captured. In this paper, we consider the more challenging incomplete information problem where dynamic pricing is applied in conjunction with learning the unknown parameters, with the objective of optimizing the cumulative revenues over a given selling horizon of length $T$. Equivalently, the goal is to minimize the regret which measures the revenue loss of the algorithm relative to the optimal expected revenue achievable under the stochastic Bass model with market size $m$ and time horizon $T$. Our main contribution is the development of an algorithm that satisfies a high probability regret guarantee of order $tilde O(m^{2/3})$; where the market size $m$ is known a priori. Moreover, we show that no algorithm can incur smaller order of loss by deriving a matching lower bound. Unlike most regret analysis results, in the present problem the market size $m$ is the fundamental driver of the complexity; our lower bound in fact, indicates that for any fixed $alpha, beta$, most non-trivial instances of the problem have constant $T$ and large $m$. We believe that this insight sets the problem of dynamic pricing under the Bass model apart from the typical i.i.d. setting and multi-armed bandit based models for dynamic pricing, which typically focus only on the asymptotics with respect to time horizon $T$.
قيم البحث
اقرأ أيضاً
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 simulated market environments. This allows consideration of market dynamics that are not analytically tractable or can not be empirically analyzed due to practical complications. Our findings implicate that the relative performance of algorithms varies substantially across different market dynamics, which confirms the intrinsic complexity of pricing and learning in the presence of competition.
Recently equal risk pricing, a framework for fair derivative pricing, was extended to consider dynamic risk measures. However, all current implementations either employ a static risk measure that violates time consistency, or are based on traditional
dynamic programming solution schemes that are impracticable in problems with a large number of underlying assets (due to the curse of dimensionality) or with incomplete asset dynamics information. In this paper, we extend for the first time a famous off-policy deterministic actor-critic deep reinforcement learning (ACRL) algorithm to the problem of solving a risk averse Markov decision process that models risk using a time consistent recursive expectile risk measure. This new ACRL algorithm allows us to identify high quality time consistent hedging policies (and equal risk prices) for options, such as basket options, that cannot be handled using traditional methods, or in context where only historical trajectories of the underlying assets are available. Our numerical experiments, which involve both a simple vanilla option and a more exotic basket option, confirm that the new ACRL algorithm can produce 1) in simple environments, nearly optimal hedging policies, and highly accurate prices, simultaneously for a range of maturities 2) in complex environments, good quality policies and prices using reasonable amount of computing resources; and 3) overall, hedging strategies that actually outperform the strategies produced using static risk measures when the risk is evaluated at later points of time.
In this paper we present an end-to-end framework for addressing the problem of dynamic pricing (DP) on E-commerce platform using methods based on deep reinforcement learning (DRL). By using four groups of different business data to represent the stat
es of each time period, we model the dynamic pricing problem as a Markov Decision Process (MDP). Compared with the state-of-the-art DRL-based dynamic pricing algorithms, our approaches make the following three contributions. First, we extend the discrete set problem to the continuous price set. Second, instead of using revenue as the reward function directly, we define a new function named difference of revenue conversion rates (DRCR). Third, the cold-start problem of MDP is tackled by pre-training and evaluation using some carefully chosen historical sales data. Our approaches are evaluated by both offline evaluation method using real dataset of Alibaba Inc., and online field experiments starting from July 2018 with thousands of items, lasting for months on Tmall.com. To our knowledge, there is no other DP field experiment using DRL before. Field experiment results suggest that DRCR is a more appropriate reward function than revenue, which is widely used by current literature. Also, continuous price sets have better performance than discrete sets and our approaches significantly outperformed the manual pricing by operation experts.
Feature-based dynamic pricing is an increasingly popular model of setting prices for highly differentiated products with applications in digital marketing, online sales, real estate and so on. The problem was formally studied as an online learning pr
oblem (Cohen et al., 2016; Javanmard & Nazerzadeh, 2019) where a seller needs to propose prices on the fly for a sequence of $T$ products based on their features $x$ while having a small regret relative to the best -- omniscient -- pricing strategy she could have come up with in hindsight. We revisit this problem and provide two algorithms (EMLP and ONSP) for stochastic and adversarial feature settings, respectively, and prove the optimal $O(dlog{T})$ regret bounds for both. In comparison, the best existing results are $Oleft(minleft{frac{1}{lambda_{min}^2}log{T}, sqrt{T}right}right)$ and $O(T^{2/3})$ respectively, with $lambda_{min}$ being the smallest eigenvalue of $mathbb{E}[xx^T]$ that could be arbitrarily close to $0$. We also prove an $Omega(sqrt{T})$ information-theoretic lower bound for a slightly more general setting, which demonstrates that knowing-the-demand-curve leads to an exponential improvement in feature-based dynamic pricing.
In this paper, we study the contextual dynamic pricing problem where the market value of a product is linear in its observed features plus some market noise. Products are sold one at a time, and only a binary response indicating success or failure of
a sale is observed. Our model setting is similar to Javanmard and Nazerzadeh [2019] except that we expand the demand curve to a semiparametric model and need to learn dynamically both parametric and nonparametric components. We propose a dynamic statistical learning and decision-making policy that combines semiparametric estimation from a generalized linear model with an unknown link and online decision-making to minimize regret (maximize revenue). Under mild conditions, we show that for a market noise c.d.f. $F(cdot)$ with $m$-th order derivative ($mgeq 2$), our policy achieves a regret upper bound of $tilde{O}_{d}(T^{frac{2m+1}{4m-1}})$, where $T$ is time horizon and $tilde{O}_{d}$ is the order that hides logarithmic terms and the dimensionality of feature $d$. The upper bound is further reduced to $tilde{O}_{d}(sqrt{T})$ if $F$ is super smooth whose Fourier transform decays exponentially. In terms of dependence on the horizon $T$, these upper bounds are close to $Omega(sqrt{T})$, the lower bound where $F$ belongs to a parametric class. We further generalize these results to the case with dynamically dependent product features under the strong mixing condition.
الأسئلة المقترحة
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
