Risk-Averse Dynamic Pricing Using Mean-Semivariance Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Risk-Averse Dynamic Pricing Using Mean-Semivariance Optimization write by Rainer Schlosser. This book was released on 2023. Risk-Averse Dynamic Pricing Using Mean-Semivariance Optimization available in PDF, EPUB and Kindle. 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.
Time-Consistent, Risk-Averse Dynamic Pricing
Time-Consistent, Risk-Averse Dynamic Pricing - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Time-Consistent, Risk-Averse Dynamic Pricing write by Rouven Schur. This book was released on 2019. Time-Consistent, Risk-Averse Dynamic Pricing available in PDF, EPUB and Kindle. 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.
Optimizing Conditional Value-at-Risk in Dynamic Pricing
Optimizing Conditional Value-at-Risk in Dynamic Pricing - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Optimizing Conditional Value-at-Risk in Dynamic Pricing write by Jochen Gönsch. This book was released on 2018. Optimizing Conditional Value-at-Risk in Dynamic Pricing available in PDF, EPUB and Kindle. 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.
A Stochastic Dynamic Pricing and Advertising Model Under Risk Aversion
A Stochastic Dynamic Pricing and Advertising Model Under Risk Aversion - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Stochastic Dynamic Pricing and Advertising Model Under Risk Aversion write by Rainer Schlosser. This book was released on 2015. A Stochastic Dynamic Pricing and Advertising Model Under Risk Aversion available in PDF, EPUB and Kindle. 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.
Risk-Averse Optimization and Control
Risk-Averse Optimization and Control - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Risk-Averse Optimization and Control write by Darinka Dentcheva. This book was released on 2024-06-16. Risk-Averse Optimization and Control available in PDF, EPUB and Kindle. 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.
