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.
Risk-Averse Dynamic Pricing Using Mean-Semivariance Optimization
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.
Risk-Averse Dynamic Arbitrage in Illiquid Markets
Risk-Averse Dynamic Arbitrage in Illiquid Markets - 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 Arbitrage in Illiquid Markets write by Somayeh Moazeni. This book was released on 2017. Risk-Averse Dynamic Arbitrage in Illiquid Markets available in PDF, EPUB and Kindle. Arguments on the existence of dynamic arbitrage and price manipulation strategies are often invoked to guide modeling price impacts of large trades. We revisit the concept of dynamic arbitrage in illiquid markets in the presence of time-varying stochastic price impact functions and a broad class of market price dynamics. We first establish a sufficient condition under which searching in the space of $ mathcal F_{0}$-measurable admissible round-trip trades is enough to attain a no-dynamic arbitrage certificate. This result simplifies identifying price impact structures that rule out dynamic arbitrage and supports the analysis in some existing literature, where its assessment is limited to the search in the set of $ mathcal F_{0}$-measurable round-trip trades. For time-varying stochastic linear price impact functions, we show that this condition is necessary and sufficient for the absence of dynamic arbitrage. The present quantitative analysis implies that a trader's opinion on the existence of dynamic arbitrage opportunities for a price impact model depends on his belief about expected future price changes and expected future price impacts, which can be revised over time by the collection of new information. This motivates us to let the existence of such arbitrage opportunities depend not only on the trader's belief about expected price movements but also on his risk attitude. We thus introduce the concept of risk-averse dynamic arbitrage using a general time-consistent dynamic risk measure and a risk-aversion threshold level. Similar sufficient conditions are studied under which searching in the space of static round-trip trades enables us to conclude on no-risk-averse dynamic arbitrage.
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.
Time-Inconsistent Control Theory with Finance Applications
Time-Inconsistent Control Theory with Finance Applications - 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-Inconsistent Control Theory with Finance Applications write by Tomas Björk. This book was released on 2021-11-02. Time-Inconsistent Control Theory with Finance Applications available in PDF, EPUB and Kindle. This book is devoted to problems of stochastic control and stopping that are time inconsistent in the sense that they do not admit a Bellman optimality principle. These problems are cast in a game-theoretic framework, with the focus on subgame-perfect Nash equilibrium strategies. The general theory is illustrated with a number of finance applications. In dynamic choice problems, time inconsistency is the rule rather than the exception. Indeed, as Robert H. Strotz pointed out in his seminal 1955 paper, relaxing the widely used ad hoc assumption of exponential discounting gives rise to time inconsistency. Other famous examples of time inconsistency include mean-variance portfolio choice and prospect theory in a dynamic context. For such models, the very concept of optimality becomes problematic, as the decision maker’s preferences change over time in a temporally inconsistent way. In this book, a time-inconsistent problem is viewed as a non-cooperative game between the agent’s current and future selves, with the objective of finding intrapersonal equilibria in the game-theoretic sense. A range of finance applications are provided, including problems with non-exponential discounting, mean-variance objective, time-inconsistent linear quadratic regulator, probability distortion, and market equilibrium with time-inconsistent preferences. Time-Inconsistent Control Theory with Finance Applications offers the first comprehensive treatment of time-inconsistent control and stopping problems, in both continuous and discrete time, and in the context of finance applications. Intended for researchers and graduate students in the fields of finance and economics, it includes a review of the standard time-consistent results, bibliographical notes, as well as detailed examples showcasing time inconsistency problems. For the reader unacquainted with standard arbitrage theory, an appendix provides a toolbox of material needed for the book.
