Risk-Averse Dynamic Pricing Using Mean-Semivariance Optimization PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Risk-Averse Dynamic Pricing Using Mean-Semivariance Optimization PDF full book. Access full book title Risk-Averse Dynamic Pricing Using Mean-Semivariance Optimization by Rainer Schlosser. Download full books in PDF and EPUB format.
Author: Rainer Schlosser
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
In many revenue management applications risk-averse decision-making is crucial. In dynamic settings, however, it is challenging to find the right balance between maximizing expected rewards and avoiding poor performances. In this paper, we consider time-consistent mean-semivariance (MSV) optimization for dynamic pricing problems within a discrete MDP framework, which are shown to be NP hard. We present a novel fixpoint-based dynamic programming approach to compute risk-sensitive feedback policies with Pareto-optimal combinations of mean and semivariance. We illustrate the effectiveness and the applicability of our concepts compared to state-of-the-art heuristics. For various numerical examples the results show that our approach clearly outperforms all other heuristics and obtains a performance guarantee with less then 0.2% optimality gap. Our approach is general and can be applied to MDPs beyond dynamic pricing.
Author: Rainer Schlosser
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
In many revenue management applications risk-averse decision-making is crucial. In dynamic settings, however, it is challenging to find the right balance between maximizing expected rewards and avoiding poor performances. In this paper, we consider time-consistent mean-semivariance (MSV) optimization for dynamic pricing problems within a discrete MDP framework, which are shown to be NP hard. We present a novel fixpoint-based dynamic programming approach to compute risk-sensitive feedback policies with Pareto-optimal combinations of mean and semivariance. We illustrate the effectiveness and the applicability of our concepts compared to state-of-the-art heuristics. For various numerical examples the results show that our approach clearly outperforms all other heuristics and obtains a performance guarantee with less then 0.2% optimality gap. Our approach is general and can be applied to MDPs beyond dynamic pricing.
Author: Rouven Schur
Publisher:
ISBN:
Category :
Languages : en
Pages : 45
Get Book Here
Book Description
Many industries use dynamic pricing on an operational level to maximize revenue from selling a fixed capacity over a finite horizon. Classical risk-neutral approaches do not accommodate the risk aversion often encountered in practice. When risk aversion is considered, time-consistency becomes an important issue. In this paper, we use a dynamic coherent risk-measure to ensure that decisions are actually implemented and only depend on states that may realize in the future. In particular, we use the risk measure Conditional Value-at-Risk (CVaR), which recently became popular in areas like finance, energy or supply chain management. A result is that the risk-averse dynamic pricing problem can be transformed to a classical, risk-neutral problem. To do so, a surprisingly simple modification of the selling probabilities suffices. Thus, all structural properties carry over. Moreover, we show that the risk-averse and the risk-neutral solution of the original problem are proportional under certain conditions, that is, their optimal decision variable and objective values are proportional, respectively. In a small numerical study, we evaluate the risk vs. revenue trade-off and compare the new approach with existing approaches from literature.This has straightforward implications for practice. On the one hand, it shows that existing dynamic pricing algorithms and systems can be kept in place and easily incorporate risk aversion. On the other hand, our results help to understand many risk-averse decision makers who often use “conservative” estimates of selling probabilities or discount optimal prices.
Author: Jochen Gönsch
Publisher:
ISBN:
Category :
Languages : en
Pages : 45
Get Book Here
Book Description
Many industries use dynamic pricing on an operational level to maximize revenue from selling a fixed capacity over a finite horizon. Classical risk-neutral approaches do not accommodate the risk aversion often encountered in practice. We add to the scarce literature on risk aversion by considering the risk measure Conditional Value-at-Risk (CVaR), which recently became popular in areas like finance, energy or supply chain management. A key aspect of this paper is selling a single unit of capacity, which is highly relevant in, for example, the real estate market. We analytically derive the optimal policy and obtain structural results. The most important managerial implication is that the risk-averse optimal price is constant over large parts of the selling horizon, whereas the price continuously declines in the standard setting of risk-neutral dynamic pricing. This offers a completely new explanation for the price-setting behavior often observed in practice. For arbitrary capacity, we develop two algorithms to efficiently compute the value function and evaluate them in a numerical study. Our results show that applying a risk-averse policy, even a static one, often yields a higher CVaR than applying a dynamic, but risk-neutral, policy.
Author: Rainer Schlosser
Publisher:
ISBN:
Category :
Languages : en
Pages : 30
Get Book Here
Book Description
This paper analyzes a dynamic pricing and advertising model for the sale of perishable products under constant absolute risk aversion. We consider a time-dependent version of Gallego and van Ryzin's (1994) model with advertising effects, accounting for marginal unit costs. We derive closed-form expressions of the optimal risk-averse pricing and advertising policies of the value function and of the certainty equivalent. The formulas provide insight into the (complex) interplay between risk-sensitive pricing and advertising decisions. Moreover, to evaluate the optimally controlled sales process over time we propose efficient simulation techniques. These are used to analyze the characteristics of different degrees of risk aversion, particularly the concentration of the profit distribution and the impact on the expected evolution of price and advertising rates.
Author: Darinka Dentcheva
Publisher: Springer
ISBN: 9783031579875
Category : Mathematics
Languages : en
Pages : 0
Get Book Here
Book Description
This book offers a comprehensive presentation of the theory and methods of risk-averse optimization and control. Problems of this type arise in finance, energy production and distribution, supply chain management, medicine, and many other areas, where not only the average performance of a stochastic system is essential, but also high-impact and low-probability events must be taken into account. The book is a self-contained presentation of the utility theory, the theory of measures of risk, including systemic and dynamic measures of risk, and their use in optimization and control models. It also covers stochastic dominance relations and their application as constraints in optimization models. Optimality conditions for problems with nondifferentiable and nonconvex functions and operators involving risk measures and stochastic dominance relations are discussed. Much attention is paid to multi-stage risk-averse optimization problems and to risk-averse Markov decision problems. Specialized algorithms for solving risk-averse optimization and control problems are presented and analyzed: stochastic subgradient methods for risk optimization, decomposition methods for dynamic problems, event cut and dual methods for stochastic dominance constraints, and policy iteration methods for control problems. The target audience is researchers and graduate students in the areas of mathematics, business analytics, insurance and finance, engineering, and computer science. The theoretical considerations are illustrated with examples, which make the book useful material for advanced courses in the area.
Author: Siddhartha Pratim Chakrabarty
Publisher: Springer Nature
ISBN: 9811985448
Category : Mathematics
Languages : en
Pages : 158
Get Book Here
Book Description
Designed as a self-contained text, this book covers a wide spectrum of topics on portfolio theory. It covers both the classical-mean-variance portfolio theory as well as non-mean-variance portfolio theory. The book covers topics such as optimal portfolio strategies, bond portfolio optimization and risk management of portfolios. In order to ensure that the book is self-contained and not dependent on any pre-requisites, the book includes three chapters on basics of financial markets, probability theory and asset pricing models, which have resulted in a holistic narrative of the topic. Retaining the spirit of the classical works of stalwarts like Markowitz, Black, Sharpe, etc., this book includes various other aspects of portfolio theory, such as discrete and continuous time optimal portfolios, bond portfolios and risk management. The increase in volume and diversity of banking activities has resulted in a concurrent enhanced importance of portfolio theory, both in terms of management perspective (including risk management) and the resulting mathematical sophistication required. Most books on portfolio theory are written either from the management perspective, or are aimed at advanced graduate students and academicians. This book bridges the gap between these two levels of learning. With many useful solved examples and exercises with solutions as well as a rigorous mathematical approach of portfolio theory, the book is useful to undergraduate students of mathematical finance, business and financial management.
Author: Tsan-Ming Choi
Publisher: Springer Science & Business Media
ISBN: 1461438691
Category : Business & Economics
Languages : en
Pages : 104
Get Book Here
Book Description
Risk analysis is crucial in stochastic supply chain models. Over the past few years, the pace has quickened for research attempting to explore risk analysis issues in supply chain management problems, while the majority of recent papers focus on conceptual framework or computational numerical analysis. Pioneered by Nobel laureate Markowitz in the 1950s, the mean-risk (MR) formulation became a fundamental theory for risk management in finance. Despite the significance and popularity of MR-related approaches in finance, their applications in studying multi-echelon supply chain management problems have only been seriously explored in recent years. While the MR approach has already been shown to be useful in conducting risk analysis in stochastic supply chain models, there is no comprehensive reference source that provides the state-of-the-art findings on this important model for supply chain management. Thus it is significant to have a book that reviews and extends the MR related works for supply chain risk analysis. This book is organized into five chapters. Chapter 1 introduces the topic, offers a timely review of various related areas, and explains why the MR approach is important for conducting supply chain risk analysis. Chapter 2 examines the single period inventory model with the mean-variance and mean-semi-deviation approaches. Extensive discussions on the efficient frontiers are also reported. Chapter 3 explores the infinite horizon multi-period inventory model with a mean-variance approach. Chapter 4 investigates the supply chain coordination problem with a versatile target sales rebate contract and a risk averse retailer possessing the mean-variance optimization objective. Chapter 5 concludes the book and discusses various promising future research directions and extensions. Every chapter can be taken as a self-contained article, and the notation within each chapter is consistently employed.
Author: Nicolas Chapados
Publisher: Springer Science & Business Media
ISBN: 1461405777
Category : Computers
Languages : en
Pages : 107
Get Book Here
Book Description
This brief offers a broad, yet concise, coverage of portfolio choice, containing both application-oriented and academic results, along with abundant pointers to the literature for further study. It cuts through many strands of the subject, presenting not only the classical results from financial economics but also approaches originating from information theory, machine learning and operations research. This compact treatment of the topic will be valuable to students entering the field, as well as practitioners looking for a broad coverage of the topic.
Author: Richard E. Oberuc
Publisher: McGraw Hill Professional
ISBN: 9780071426695
Category : Business & Economics
Languages : en
Pages : 344
Get Book Here
Book Description
Publisher Description
Author: Merve Merakli
Publisher:
ISBN:
Category :
Languages : en
Pages : 138
Get Book Here
Book Description
Risk-averse stochastic programming provides means to incorporate a wide range of risk attitudes into decision making. Pioneered by the advances in financial optimization, several risk measures such as Value-at-Risk (VaR) and Conditional-Value-at-Risk (CVaR) are employed in risk-averse stochastic programming for a variety of application areas. In this work, we consider risk-averse modeling approaches for stochastic multicriteria and stochastic sequential decision-making problems. First, we propose a new multivariate definition for CVaR as a set of vectors. We analyze its properties and establish that the new definition remedies some potential drawbacks of the existing definitions for discrete random variables. Motivated by the computational challenges in the optimization of vector-valued multivariate definitions of CVaR, next, we study two-stage stochastic programming problems with multivariate risk constraints utilizing a scalarization scheme. We formulate this problem as a mixed-integer program (MIP) and devise two delayed cut generation algorithms. The effectiveness of the proposed modeling approach and solution methods are demonstrated on a pre-disaster relief network design problem. Finally, we study the Markov Decision Processes (MDPs) under cost and transition probability uncertainty with the objective of optimizing the VaR associated with the expected performance of an MDP model. Based on a sampling approach, we provide an MIP formulation and a branch-and-cut algorithm, and demonstrate our proposed methods on an inventory management problem for long-term humanitarian relief operations.
