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Author: Rouven Schur
Publisher:
ISBN:
Category :
Languages : en
Pages : 45
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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: 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: Rainer Schlosser
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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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: Somayeh Moazeni
Publisher:
ISBN:
Category :
Languages : en
Pages : 24
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Book Description
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.
Author: Rainer Schlosser
Publisher:
ISBN:
Category :
Languages : en
Pages : 30
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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: Tomas Björk
Publisher: Springer Nature
ISBN: 3030818438
Category : Mathematics
Languages : en
Pages : 328
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Book Description
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.
Author: Maria Pilar Martinez-Ruiz
Publisher: Frontiers Media SA
ISBN: 2889664856
Category : Science
Languages : en
Pages : 147
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Book Description
Author: Chenghu Ma
Publisher: World Scientific
ISBN: 184816632X
Category : Business & Economics
Languages : en
Pages : 818
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Book Description
This book provides a broad introduction to modern asset pricing theory. The theory is self-contained and unified in presentation. Both the no-arbitrage and the general equilibrium approaches of asset pricing theory are treated coherently within the general equilibrium framework. It fills a gap in the body of literature on asset pricing for being both advanced and comprehensive. The absence of arbitrage opportunities represents a necessary condition for equilibrium in the financial markets. However, the absence of arbitrage is not a sufficient condition for establishing equilibrium. These interrelationships are overlooked by the proponents of the no-arbitrage approach to asset pricing.This book also tackles recent advancement on inversion problems raised in asset pricing theory, which include the information role of financial options and the information content of term structure of interest rates and interest rates contingent claims.The inclusion of the proofs and derivations to enhance the transparency of the underlying arguments and conditions for the validity of the economic theory made it an ideal advanced textbook or reference book for graduate students specializing in financial economics and quantitative finance. The detailed explanations will capture the interest of the curious reader, and it is complete enough to provide the necessary background material needed to delve deeper into the subject and explore the research literature.Postgraduate students in economics with a good grasp of calculus, linear algebra, and probability and statistics will find themselves ready to tackle topics covered in this book. They will certainly benefit from the mathematical coverage in stochastic processes and stochastic differential equation with applications in finance. Postgraduate students in financial mathematics and financial engineering will also benefit, not only from the mathematical tools introduced in this book, but also from the economic ideas underpinning the economic modeling of financial markets.Both these groups of postgraduate students will learn the economic issues involved in financial modeling. The book can be used as an advanced text for Masters and PhD students in all subjects of financial economics, financial mathematics, mathematical finance, and financial engineering. It is also an ideal reference for practitioners and researchers in the subjects.
Author: Sumru Altug
Publisher: Cambridge University Press
ISBN: 1139474367
Category : Business & Economics
Languages : en
Pages : 686
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Book Description
This introduction to general equilibrium modelling takes an integrated approach to the analysis of macroeconomics and finance. It provides students, practitioners, and policymakers with an easily accessible set of tools that can be used to analyze a wide range of economic phenomena. Key features: • Provides a consistent framework for understanding dynamic economic models • Introduces key concepts in finance in a discrete time setting • Develops simple recursive approach for analyzing a variety of problems in a dynamic, stochastic environment • Sequentially builds up the analysis of consumption, production, and investment models to study their implications for allocations and asset prices • Reviews business cycle analysis and the business cycle implications of monetary and international models • Covers latest research on asset pricing in overlapping generations models and on models with borrowing constraints and transaction costs • Includes end-of-chapter exercises allowing readers to monitor their understanding of each topic Online resources are available at www.cambridge.org/altug_labadie
Author: Mehiddin Al-Baali
Publisher: Springer
ISBN: 3319176897
Category : Mathematics
Languages : en
Pages : 351
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Book Description
Presenting the latest findings in the field of numerical analysis and optimization, this volume balances pure research with practical applications of the subject. Accompanied by detailed tables, figures, and examinations of useful software tools, this volume will equip the reader to perform detailed and layered analysis of complex datasets. Many real-world complex problems can be formulated as optimization tasks. Such problems can be characterized as large scale, unconstrained, constrained, non-convex, non-differentiable, and discontinuous, and therefore require adequate computational methods, algorithms, and software tools. These same tools are often employed by researchers working in current IT hot topics such as big data, optimization and other complex numerical algorithms on the cloud, devising special techniques for supercomputing systems. The list of topics covered include, but are not limited to: numerical analysis, numerical optimization, numerical linear algebra, numerical differential equations, optimal control, approximation theory, applied mathematics, algorithms and software developments, derivative free optimization methods and programming models. The volume also examines challenging applications to various types of computational optimization methods which usually occur in statistics, econometrics, finance, physics, medicine, biology, engineering and industrial sciences.
Author: Kenneth J. Singleton
Publisher: Princeton University Press
ISBN: 1400829232
Category : Business & Economics
Languages : en
Pages : 497
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Book Description
Written by one of the leading experts in the field, this book focuses on the interplay between model specification, data collection, and econometric testing of dynamic asset pricing models. The first several chapters provide an in-depth treatment of the econometric methods used in analyzing financial time-series models. The remainder explores the goodness-of-fit of preference-based and no-arbitrage models of equity returns and the term structure of interest rates; equity and fixed-income derivatives prices; and the prices of defaultable securities. Singleton addresses the restrictions on the joint distributions of asset returns and other economic variables implied by dynamic asset pricing models, as well as the interplay between model formulation and the choice of econometric estimation strategy. For each pricing problem, he provides a comprehensive overview of the empirical evidence on goodness-of-fit, with tables and graphs that facilitate critical assessment of the current state of the relevant literatures. As an added feature, Singleton includes throughout the book interesting tidbits of new research. These range from empirical results (not reported elsewhere, or updated from Singleton's previous papers) to new observations about model specification and new econometric methods for testing models. Clear and comprehensive, the book will appeal to researchers at financial institutions as well as advanced students of economics and finance, mathematics, and science.
