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On Two Utility Maximization Problems
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Book Synopsis On Two Utility Maximization Problems by : Anastasiya Tanana
Download or read book On Two Utility Maximization Problems written by Anastasiya Tanana and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation studies two expected utility maximization problems from mathematical finance. The first project (Chapter 2) deals with a single-agent utility maximization under constraints on intertemporal consumption; the second project (Chapter 3) studies Nash equilibria in an N-player game of utility maximization under relative performance criteria. The main and unifying approach to the two problems is convex duality in a semimartingale market model. Utility maximization under ratchet and drawdown constraints on consumption in incomplete semimartingale markets. We consider the value function associated with this concave optimization problem as having two parameters: the initial wealth and the essential lower bound on consumption rate process. In order to rigorously formulate the constraints and define the primal domains for optimization in the general setting of semimartingale markets and optional consumption plans, we introduce a natural extension of the notion of running maximum to arbitrary non-negative optional processes. The dual domains for optimization are characterized in terms of solidity of the set of equivalent martingale deflators with respect to an ordering that is introduced on the set of non-negative optional processes. The abstract duality result obtained in the general incomplete market case is used in order to derive a more detailed characterization of solutions in the complete market case. Utility maximization under relative performance criteria of multiplicative form. In the first part of this project we consider the case of a complete semimartingale market. For a large class of players’ utility functions, a general characterization of Nash equilibria for a given initial wealth vector is provided in terms of invertibility of a map from R [superscript N] to R [superscript N]. As a consequence of the general theorem, we derive existence and uniqueness of Nash equilibria for an arbitrary initial wealth vector, as well as their convergence, in two special cases. The second part studies the case of CRRA utility functions in an incomplete Itô-process market model. We establish a one-to-one correspondence between Nash equilibria satisfying a certain integrability condition and solutions of a BSDE when relative risk aversions of players are small (less than 1) and linear constraints on trading strategies are allowed
Book Synopsis Utility Maximization Problem by : Fouad Sabry
Download or read book Utility Maximization Problem written by Fouad Sabry and published by One Billion Knowledgeable. This book was released on 2024-02-06 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is Utility Maximization Problem Jeremy Bentham and John Stuart Mill, both utilitarian philosophers, were the ones who initially devised the concept of utility maximization. The utility maximization problem is a challenge that consumers encounter in the field of microeconomics. This problem pertains to the question, "How should I spend my money in order to maximize my utility?" It falls within the category of optimal choice problems. It is the process of deciding how much of each available commodity or service to consume, taking into account a limitation on overall spending (income), the cost of the goods, and the preferences of the individual. How you will benefit (I) Insights, and validations about the following topics: Chapter 1: Utility maximization problem Chapter 2: Utility Chapter 3: Indifference curve Chapter 4: Consumer choice Chapter 5: Budget constraint Chapter 6: Income-consumption curve Chapter 7: Marshallian demand function Chapter 8: Arrow-Debreu model Chapter 9: Fundamental theorems of welfare economics Chapter 10: Revealed preference Chapter 11: Indirect utility function Chapter 12: Hicksian demand function Chapter 13: Corner solution Chapter 14: Local nonsatiation Chapter 15: Sonnenschein-Mantel-Debreu theorem Chapter 16: Competitive equilibrium Chapter 17: Quasilinear utility Chapter 18: Preference (economics) Chapter 19: Fair item allocation Chapter 20: Dixit-Stiglitz model Chapter 21: Abstract economy (II) Answering the public top questions about utility maximization problem. (III) Real world examples for the usage of utility maximization problem in many fields. Who this book is for Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Utility Maximization Problem.
Book Synopsis Utility Maximization in Nonconvex Wireless Systems by : Johannes Brehmer
Download or read book Utility Maximization in Nonconvex Wireless Systems written by Johannes Brehmer and published by Springer Science & Business Media. This book was released on 2012-03-17 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph develops a framework for modeling and solving utility maximization problems in nonconvex wireless systems. The first part develops a model for utility optimization in wireless systems. The model is general enough to encompass a wide array of system configurations and performance objectives. Based on the general model, a set of methods for solving utility maximization problems is developed in the second part of the book. The development is based on a careful examination of the properties that are required for the application of each method. This part focuses on problems whose initial formulation does not allow for a solution by standard methods and discusses alternative approaches. The last part presents two case studies to demonstrate the application of the proposed framework. In both cases, utility maximization in multi-antenna broadcast channels is investigated.
Book Synopsis Utility Maximization in Multiuser, Multicarrier, Communication Systems by : Haleema Mehmood
Download or read book Utility Maximization in Multiuser, Multicarrier, Communication Systems written by Haleema Mehmood and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation addresses non-convex utility-maximization problems in multiuser, multicarrier communications systems. Utility maximization is an effective tool for communication system design. Utility functions are used to translate user or design preferences to optimization objectives. Physical-layer resource allocation in a communication system is then based on maximizing the utility of the system. This dissertations formulates a utility-maximization problem with a rate region constraint on the rate vectors. It considers various discrete optimization problems for multiuser, multicarrier communications systems. It presents algorithms that find utility-maximizing rate tuples for concave and non-concave utility functions over rate regions of Gaussian vector multiuser channels. The non-concave functions considered are staircase and sigmoidal utility functions that are widely used utility models for multimedia applications. Using a branch-and-bound method, a sequence of bounds on the optimal objective function value is obtained that converges to the global maximum sum of utilities. At each step, the algorithm solves a concave subproblem for multiuser power allocation using dual decomposition. For multicarrier systems, further decomposition of the Lagrangian across the subcarriers provides a low complexity method for utility maximization. The second part of this dissertation presents the concept of revenue potential as a tool for Internet service providers for revenue-based power allocation. Broadband Internet service providers are for-profit companies. From their perspective, utility of a multiuser channel is the total price they can charge their customers for provision of services. Broadband price functions are generally staircase functions of advertised data rates. The problem of finding the revenue potential of a DSL binder is a utility-maximization problem with a staircase utility function. The problem for the crosstalking DSLs is solved using the branch-and-bound method. A serious crosstalking problem arises in mixed deployments of vectored DSLs, sometimes known as G. Vector, and legacy DSLs. Such deployments require rate control on unvectored lines to realize vectoring gains. Revenue potential is used to determine the optimal-revenue rate-limits for unvectored lines. A strategy that limits the rates offered to the unvectored customers is shown to increase long-term revenue for the ISP. The third part of this dissertation presents a spiderweb plotting technique for multidimensional rate regions. This technique is useful for visualizing subsets of high-dimensional rate regions on a two-dimensional plot. Utility maximization is an alternative to building such rate regions and returns a single useful point instead of multiple data points. Both techniques are useful in different applied contexts. The last part of this dissertation considers a problem of joint user-clustering and bit-allocation for coaxial cable systems. The problem arises in next-generation coaxial cable systems, sometimes known as DOCSIS 3.1, with multicarrier modulation and adaptive bit loading. Users need to be grouped together and assigned bit profiles to maximize spectral efficiency. The problem is a discrete, non-convex, utility-maximization problem. A greedy, coordinate-ascent algorithm is presented to find clustering solutions to the utility-maximization problem. A comparison with optimal solutions found by exhaustive search shows that the algorithm gives close to optimal performance.
Book Synopsis Utility Maximization in Nonconvex Wireless Systems by : Johannes Brehmer
Download or read book Utility Maximization in Nonconvex Wireless Systems written by Johannes Brehmer and published by Springer Science & Business Media. This book was released on 2012-03-15 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph develops a framework for modeling and solving utility maximization problems in nonconvex wireless systems. The first part develops a model for utility optimization in wireless systems. The model is general enough to encompass a wide array of system configurations and performance objectives. Based on the general model, a set of methods for solving utility maximization problems is developed in the second part of the book. The development is based on a careful examination of the properties that are required for the application of each method. This part focuses on problems whose initial formulation does not allow for a solution by standard methods and discusses alternative approaches. The last part presents two case studies to demonstrate the application of the proposed framework. In both cases, utility maximization in multi-antenna broadcast channels is investigated.
Book Synopsis Utility Maximization with Consumption Habit Formation in Incomplete Markets by : Xiang Yu
Download or read book Utility Maximization with Consumption Habit Formation in Incomplete Markets written by Xiang Yu and published by . This book was released on 2012 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation studies a class of path-dependent stochastic control problems with applications to Finance. In particular, we solve the open problem of the continuous time expected utility maximization with addictive consumption habit formation in incomplete markets under two independent scenarios. In the first project, we study the continuous time utility optimization problem with consumption habit formation in general incomplete semimartingale financial markets. Introducing the set of auxiliary state processes and the modified dual space, we embed our original problem into an abstract time-separable utility maximization problem with a shadow random endowment on the product space [mathematic equation] We establish existence and uniqueness of the optimal solution using convex duality by defining the primal value function as depending on two variables, i.e., the initial wealth and the initial standard of living. We also provide market independent sufficient conditions both on the stochastic discounting processes of the habit formation process and on the utility function for the well-posedness of our original optimization problem. Under the same assumptions, we can carefully modify the classical proofs in the approach of convex duality analysis when the auxiliary dual process is not necessarily integrable. In the second project, we examine an example of the optimal investment and consumption problem with both habit-formation and partial observations in incomplete markets driven by Itô processes. The individual investor develops addictive consumption habits gradually while only observing the market stock prices but not the instantaneous rates of return, which follow an Ornstein-Uhlenbeck process. Applying the Kalman-Bucy filtering theorem and Dynamic Programming arguments, we solve the associated Hamilton-Jacobi-Bellman(HJB) equation fully explicitly for this path dependent stochastic control problem in the case of power utility preferences. We provide the optimal investment and consumption policy in explicit feedback form using rigorous verification arguments.
Book Synopsis Utility Maximization, Choice and Preference by : Fuad Aleskerov
Download or read book Utility Maximization, Choice and Preference written by Fuad Aleskerov and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: The utility maximization paradigm forms the basis of many economic, psychological, cognitive and behavioral models. However, numerous examples have revealed the deficiencies of the concept. This book helps to overcome those deficiencies by taking into account insensitivity of measurement threshold and context of choice. The second edition has been updated to include the most recent developments and a new chapter on classic and new results for infinite sets.
Book Synopsis Handbook of Utility Theory by : Salvador Barbera
Download or read book Handbook of Utility Theory written by Salvador Barbera and published by Springer Science & Business Media. This book was released on 1998 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: The standard rationality hypothesis implies that behaviour can be represented as the maximization of a suitably restricted utility function. This hypothesis lies at the heart of a large body of recent work in economics, of course, but also in political science, ethics, and other major branches of social sciences. Though the utility maximization hypothesis is venerable, it remains an area of active research. Moreover, some fundamental conceptual problems remain unresolved, or at best have resolutions that are too recent to have achieved widespread understanding among social scientists. The main purpose of the Handbook of Utility Theory is to make recent developments in the area more accessible. The editors selected a number of specific topics, and invited contributions from researchers whose work had come to their attention. Therefore, the list of topics and contributions is largely the editors' responsibility. Each contributor's chapter has been refereed, and revised according to the referees' remarks. This is the first volume of a two volume set, with the second volume focusing on extensions of utility theory.
Download or read book Utility written by Fouad Sabry and published by One Billion Knowledgeable. This book was released on 2024-02-05 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is Utility In economics, utility is a measure of the satisfaction that a certain person has from a certain state of the world. Over time, the term has been used in two different meanings.The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism, by moral philosophers such as Jeremy Bentham and John Stuart Mill. In this context, the utilities of different people in the same state are comparable. In particular, one can compute the sum of all peoples' utilities in each state, and choose the state in which the sum is maximized; this leads to the utilitarian rule of social choice.The term has been adapted and reapplied within neoclassical economics, which dominates modern economic theory, as a representation of a consumer's ordinal preferences over a choice set. In this context, utility is not comparable across different consumers or possessing a cardinal interpretation. In fact, every monotone transformation of a utility function represents the same ordinal ranking over the alternatives, and thus is equivalent from the neoclassical economics point of view. In game theory, too, utility is used in the same meaning. This concept of utility is personal and based on choice rather than on pleasure received, and so requires fewer behavioral assumptions than the original concept. How you will benefit (I) Insights, and validations about the following topics: Chapter 1: Utility Chapter 2: Indifference curve Chapter 3: Arrow's impossibility theorem Chapter 4: Social welfare function Chapter 5: Consumer choice Chapter 6: Welfare economics Chapter 7: Expected utility hypothesis Chapter 8: Utility maximization problem Chapter 9: Marshallian demand function Chapter 10: Ordinal utility Chapter 11: Cardinal utility Chapter 12: Revealed preference Chapter 13: Constant elasticity of substitution Chapter 14: Quasilinear utility Chapter 15: Von Neumann-Morgenstern utility theorem Chapter 16: Preference (economics) Chapter 17: Preference Chapter 18: Debreu's representation theorems Chapter 19: Multi-attribute utility Chapter 20: Dichotomous preferences Chapter 21: Responsive set extension (II) Answering the public top questions about utility. (III) Real world examples for the usage of utility in many fields. Who this book is for Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Utility.
Book Synopsis Intermediate Microeconomics by : Patrick M. Emerson
Download or read book Intermediate Microeconomics written by Patrick M. Emerson and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Utility Theory by : Salvador Barbera
Download or read book Handbook of Utility Theory written by Salvador Barbera and published by Springer Science & Business Media. This book was released on 2004-03-31 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: The standard rationality hypothesis is that behaviour can be represented as the maximization of a suitably restricted utility function. This hypothesis lies at the heart of a large body of recent work in economics, of course, but also in political science, ethics, and other major branches of the social sciences. Though this hypothesis of utility maximization deserves our continued respect, finding further refinements and developing new critiques remain areas of active research. In fact, many fundamental conceptual problems remain unsettled. Where others have been resolved, their resolutions may be too recent to have achieved widespread understanding among social scientists. Last but not least, a growing number of papers attempt to challenge the rationality hypothesis head on, at least in its more orthodox formulation. The main purpose of this Handbook is to make more widely available some recent developments in the area. Yet we are well aware that the final chapter of a handbook like this can never be written as long as the area of research remains active, as is certainly the case with utility theory. The editors originally selected a list of topics that seemed ripe enough at the time that the book was planned. Then they invited contributions from researchers whose work had come to their attention. So the list of topics and contributors is largely the editors' responsibility, although some potential con tributors did decline our invitation. Each chapter has also been refereed, and often significantly revised in the light of the referees' remarks.
Book Synopsis Utility Maximization, Choice and Preference by : Fuad Aleskerov
Download or read book Utility Maximization, Choice and Preference written by Fuad Aleskerov and published by Springer Science & Business Media. This book was released on 2007-08-09 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: The utility maximization paradigm forms the basis of many economic, psychological, cognitive and behavioral models. However, numerous examples have revealed the deficiencies of the concept. This book helps to overcome those deficiencies by taking into account insensitivity of measurement threshold and context of choice. The second edition has been updated to include the most recent developments and a new chapter on classic and new results for infinite sets.
Book Synopsis Contemporary Issues in Group Decision and Negotiation by : Danielle Costa Morais
Download or read book Contemporary Issues in Group Decision and Negotiation written by Danielle Costa Morais and published by Springer Nature. This book was released on 2021-06-02 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 21st International Conference on Group Decision and Negotiation, GDN 2021, which was planned to be held in Toronto, ON, Canada, during June 6–10, 2021. The conference was held virtually due to the COVID-19 pandemic. The field of Group Decision and Negotiation focuses on decision processes with at least two participants and a common goal but conflicting individual goals. Research areas of Group Decision and Negotiation include electronic negotiations, experiments, the role of emotions in group decision and negotiations, preference elicitation and decision support for group decisions and negotiations, and conflict resolution principles. The 12 full papers presented in this volume were carefully reviewed and selected from 74 submissions. They were organized in topical sections as follows: pandemic responses; preference modeling for group decision and negotiation; conflict resolution; and collaborative decision making processes.
Book Synopsis International Macroeconomics by : Stephanie Schmitt-Grohé
Download or read book International Macroeconomics written by Stephanie Schmitt-Grohé and published by Princeton University Press. This book was released on 2022-09-06 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: An essential introduction to one of the most timely and important subjects in economics International Macroeconomics presents a rigorous and theoretically elegant treatment of real-world international macroeconomic problems, incorporating the latest economic research while maintaining a microfounded, optimizing, and dynamic general equilibrium approach. This one-of-a-kind textbook introduces a basic model and applies it to fundamental questions in international economics, including the determinants of the current account in small and large economies, processes of adjustment to shocks, the determinants of the real exchange rate, the role of fixed and flexible exchange rates in models with nominal rigidities, and interactions between monetary and fiscal policy. The book confronts theoretical predictions using actual data, highlighting both the power and limits of given theories and encouraging critical thinking. Provides a rigorous and elegant treatment of fundamental questions in international macroeconomicsBrings undergraduate and master’s instruction in line with modern economic researchFollows a microfounded, optimizing, and dynamic general equilibrium approachAddresses fundamental questions in international economics, such as the role of capital controls in the presence of financial frictions and balance-of-payments crisesUses real-world data to test the predictions of theoretical modelsFeatures a wealth of exercises at the end of each chapter that challenge students to hone their theoretical skills and scrutinize the empirical relevance of modelsAccompanied by a website with lecture slides for every chapter
Book Synopsis A Short Course in Intermediate Microeconomics with Calculus by : Roberto Serrano
Download or read book A Short Course in Intermediate Microeconomics with Calculus written by Roberto Serrano and published by Cambridge University Press. This book was released on 2012-11-30 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for an intermediate level course in microeconomics that uses calculus throughout. Most of the competition either uses no calculus or relegates the math to footnotes and appendices. The text also focuses on theory rather than empirical data. To motivate the analysis, the authors include references to real events and firms, with no distracting separate boxes.
Book Synopsis Continuous-time Stochastic Control and Optimization with Financial Applications by : Huyên Pham
Download or read book Continuous-time Stochastic Control and Optimization with Financial Applications written by Huyên Pham and published by Springer Science & Business Media. This book was released on 2009-05-28 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic optimization problems arise in decision-making problems under uncertainty, and find various applications in economics and finance. On the other hand, problems in finance have recently led to new developments in the theory of stochastic control. This volume provides a systematic treatment of stochastic optimization problems applied to finance by presenting the different existing methods: dynamic programming, viscosity solutions, backward stochastic differential equations, and martingale duality methods. The theory is discussed in the context of recent developments in this field, with complete and detailed proofs, and is illustrated by means of concrete examples from the world of finance: portfolio allocation, option hedging, real options, optimal investment, etc. This book is directed towards graduate students and researchers in mathematical finance, and will also benefit applied mathematicians interested in financial applications and practitioners wishing to know more about the use of stochastic optimization methods in finance.
Book Synopsis A Course in Microeconomic Theory by : David M. Kreps
Download or read book A Course in Microeconomic Theory written by David M. Kreps and published by Princeton University Press. This book was released on 2020-06-23 with total page 869 pages. Available in PDF, EPUB and Kindle. Book excerpt: David M. Kreps has developed a text in microeconomics that is both challenging and "user-friendly." The work is designed for the first-year graduate microeconomic theory course and is accessible to advanced undergraduates as well. Placing unusual emphasis on modern noncooperative game theory, it provides the student and instructor with a unified treatment of modern microeconomic theory--one that stresses the behavior of the individual actor (consumer or firm) in various institutional settings. The author has taken special pains to explore the fundamental assumptions of the theories and techniques studied, pointing out both strengths and weaknesses. The book begins with an exposition of the standard models of choice and the market, with extra attention paid to choice under uncertainty and dynamic choice. General and partial equilibrium approaches are blended, so that the student sees these approaches as points along a continuum. The work then turns to more modern developments. Readers are introduced to noncooperative game theory and shown how to model games and determine solution concepts. Models with incomplete information, the folk theorem and reputation, and bilateral bargaining are covered in depth. Information economics is explored next. A closing discussion concerns firms as organizations and gives readers a taste of transaction-cost economics.
