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Consumption And Investment Optimization Under Constraints
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Book Synopsis Optimal Consumption and Investment with Bankruptcy by : Suresh P. Sethi
Download or read book Optimal Consumption and Investment with Bankruptcy written by Suresh P. Sethi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents papers on continuous-time consumption investment models by Suresh Sethi and various co-authors. Sir Isaac Newton said that he saw so far because he stood on the shoulders of gi ants. Giants upon whose shoulders Professor Sethi and colleagues stand are Robert Merton, particularly Merton's (1969, 1971, 1973) seminal papers, and Paul Samuelson, particularly Samuelson (1969). Karatzas, Lehoczky, Sethi and Shreve (1986), henceforth KLSS, re produced here as Chapter 2, reexamine the model proposed by Mer ton. KLSS use methods of modern mathematical analysis, taking care to prove the existence of integrals, check the existence and (where appro priate) the uniqueness of solutions to equations, etc. KLSS find that un der some conditions Merton's solution is correct; under others, it is not. In particular, Merton's solution for aHARA utility-of-consumption is correct for some parameter values and not for others. The problem with Merton's solution is that it sometimes violates the constraints against negative wealth and negative consumption stated in Merton (1969) and presumably applicable in Merton (1971 and 1973). This not only affects the solution at the zero-wealth, zero-consumption boundaries, but else where as well. Problems with Merton's solution are analyzed in Sethi and Taksar (1992), reproduced here as Chapter 3.
Book Synopsis Paris-Princeton Lectures on Mathematical Finance 2002 by : René Carmona
Download or read book Paris-Princeton Lectures on Mathematical Finance 2002 written by René Carmona and published by Springer Science & Business Media. This book was released on 2003 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Investment-consumption Models with Constraints by : Thaleia Zariphopoulou
Download or read book Optimal Investment-consumption Models with Constraints written by Thaleia Zariphopoulou and published by . This book was released on 1989 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Essays on Portfolio Optimization and ESG Ratings under Risk Constraints and Incomplete Information by : Janke, Oliver
Download or read book Essays on Portfolio Optimization and ESG Ratings under Risk Constraints and Incomplete Information written by Janke, Oliver and published by Lehmanns Media. This book was released on with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we analyze various problems of dynamic portfolio optimization as well as green capital requirements under risk constraints and incomplete information. First, we examine the problem of optimal expected utility under the constraint of a utility-based shortfall risk measure in an incomplete market. The existence and uniqueness of an optimal solution to the problem are shown using a Lagrange multiplier and duality methods. Second, we consider the optimization problem under various levels of the investor’s information. By using martingale representation theorems, we demonstrate the existence and uniqueness of optimal solutions, which differ in their market dynamics. Third, we analyze the effects of green- and brownwashing on banks’ lending to firms, on the regulator’s deposit insurance subsidy, and on carbon emissions under different green capital requirement functions. Furthermore, we show that green capital requirements may compromise financial stability.
Book Synopsis Optimization Methods in Finance by : Gerard Cornuejols
Download or read book Optimization Methods in Finance written by Gerard Cornuejols and published by Cambridge University Press. This book was released on 2006-12-21 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization models play an increasingly important role in financial decisions. This is the first textbook devoted to explaining how recent advances in optimization models, methods and software can be applied to solve problems in computational finance more efficiently and accurately. Chapters discussing the theory and efficient solution methods for all major classes of optimization problems alternate with chapters illustrating their use in modeling problems of mathematical finance. The reader is guided through topics such as volatility estimation, portfolio optimization problems and constructing an index fund, using techniques such as nonlinear optimization models, quadratic programming formulations and integer programming models respectively. The book is based on Master's courses in financial engineering and comes with worked examples, exercises and case studies. It will be welcomed by applied mathematicians, operational researchers and others who work in mathematical and computational finance and who are seeking a text for self-learning or for use with courses.
Book Synopsis Handbooks in Operations Research and Management Science: Financial Engineering by : John R. Birge
Download or read book Handbooks in Operations Research and Management Science: Financial Engineering written by John R. Birge and published by Elsevier. This book was released on 2007-11-16 with total page 1026 pages. Available in PDF, EPUB and Kindle. Book excerpt: The remarkable growth of financial markets over the past decades has been accompanied by an equally remarkable explosion in financial engineering, the interdisciplinary field focusing on applications of mathematical and statistical modeling and computational technology to problems in the financial services industry. The goals of financial engineering research are to develop empirically realistic stochastic models describing dynamics of financial risk variables, such as asset prices, foreign exchange rates, and interest rates, and to develop analytical, computational and statistical methods and tools to implement the models and employ them to design and evaluate financial products and processes to manage risk and to meet financial goals. This handbook describes the latest developments in this rapidly evolving field in the areas of modeling and pricing financial derivatives, building models of interest rates and credit risk, pricing and hedging in incomplete markets, risk management, and portfolio optimization. Leading researchers in each of these areas provide their perspective on the state of the art in terms of analysis, computation, and practical relevance. The authors describe essential results to date, fundamental methods and tools, as well as new views of the existing literature, opportunities, and challenges for future research.
Book Synopsis Stochastic Analysis, Filtering, and Stochastic Optimization by : George Yin
Download or read book Stochastic Analysis, Filtering, and Stochastic Optimization written by George Yin and published by Springer Nature. This book was released on 2022-04-22 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of research works to honor the late Professor Mark H.A. Davis, whose pioneering work in the areas of Stochastic Processes, Filtering, and Stochastic Optimization spans more than five decades. Invited authors include his dissertation advisor, past collaborators, colleagues, mentees, and graduate students of Professor Davis, as well as scholars who have worked in the above areas. Their contributions may expand upon topics in piecewise deterministic processes, pathwise stochastic calculus, martingale methods in stochastic optimization, filtering, mean-field games, time-inconsistency, as well as impulse, singular, risk-sensitive and robust stochastic control.
Book Synopsis Linear and Mixed Integer Programming for Portfolio Optimization by : Renata Mansini
Download or read book Linear and Mixed Integer Programming for Portfolio Optimization written by Renata Mansini and published by Springer. This book was released on 2015-06-10 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents solutions to the general problem of single period portfolio optimization. It introduces different linear models, arising from different performance measures, and the mixed integer linear models resulting from the introduction of real features. Other linear models, such as models for portfolio rebalancing and index tracking, are also covered. The book discusses computational issues and provides a theoretical framework, including the concepts of risk-averse preferences, stochastic dominance and coherent risk measures. The material is presented in a style that requires no background in finance or in portfolio optimization; some experience in linear and mixed integer models, however, is required. The book is thoroughly didactic, supplementing the concepts with comments and illustrative examples.
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 Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications by : Łukasz Delong
Download or read book Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications written by Łukasz Delong and published by Springer Science & Business Media. This book was released on 2013-06-12 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Backward stochastic differential equations with jumps can be used to solve problems in both finance and insurance. Part I of this book presents the theory of BSDEs with Lipschitz generators driven by a Brownian motion and a compensated random measure, with an emphasis on those generated by step processes and Lévy processes. It discusses key results and techniques (including numerical algorithms) for BSDEs with jumps and studies filtration-consistent nonlinear expectations and g-expectations. Part I also focuses on the mathematical tools and proofs which are crucial for understanding the theory. Part II investigates actuarial and financial applications of BSDEs with jumps. It considers a general financial and insurance model and deals with pricing and hedging of insurance equity-linked claims and asset-liability management problems. It additionally investigates perfect hedging, superhedging, quadratic optimization, utility maximization, indifference pricing, ambiguity risk minimization, no-good-deal pricing and dynamic risk measures. Part III presents some other useful classes of BSDEs and their applications. This book will make BSDEs more accessible to those who are interested in applying these equations to actuarial and financial problems. It will be beneficial to students and researchers in mathematical finance, risk measures, portfolio optimization as well as actuarial practitioners.
Book Synopsis Stochastic Analysis, Control, Optimization and Applications by : William M. McEneaney
Download or read book Stochastic Analysis, Control, Optimization and Applications written by William M. McEneaney and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: In view of Professor Wendell Fleming's many fundamental contributions, his profound influence on the mathematical and systems theory communi ties, his service to the profession, and his dedication to mathematics, we have invited a number of leading experts in the fields of control, optimiza tion, and stochastic systems to contribute to this volume in his honor on the occasion of his 70th birthday. These papers focus on various aspects of stochastic analysis, control theory and optimization, and applications. They include authoritative expositions and surveys as well as research papers on recent and important issues. The papers are grouped according to the following four major themes: (1) large deviations, risk sensitive and Hoc control, (2) partial differential equations and viscosity solutions, (3) stochastic control, filtering and parameter esti mation, and (4) mathematical finance and other applications. We express our deep gratitude to all of the authors for their invaluable contributions, and to the referees for their careful and timely reviews. We thank Harold Kushner for having graciously agreed to undertake the task of writing the foreword. Particular thanks go to H. Thomas Banks for his help, advice and suggestions during the entire preparation process, as well as for the generous support of the Center for Research in Scientific Computation. The assistance from the Birkhauser professional staff is also greatly appreciated.
Book Synopsis Lectures on the Mathematics of Finance by : Ioannis Karatzas
Download or read book Lectures on the Mathematics of Finance written by Ioannis Karatzas and published by American Mathematical Soc.. This book was released on 1997 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, the author discusses the main aspects of mathematical finance. These include, arbitrage, hedging and pricing of contingent claims, portfolio optimization, incomplete and/or constrained markets, equilibrium, and transaction costs. The book outlines advances made possible during the last fifteen years due to the methodologies of stochastic analysis and control. Readers are presented with current research, and open problems are suggested. This tutorial survey of the rapidly expanding field of mathematical finance is addressed primarily to graduate students in mathematics. Familiarity is assumed with stochastic analysis and parabolic partial differential equations. The text makes significant use of students' mathematical skills, but always in connection with interesting applied problems.
Book Synopsis Mathematical Modelling and Numerical Methods in Finance by : Alain Bensoussan
Download or read book Mathematical Modelling and Numerical Methods in Finance written by Alain Bensoussan and published by Elsevier. This book was released on 2009-06-16 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical finance is a prolific scientific domain in which there exists a particular characteristic of developing both advanced theories and practical techniques simultaneously. Mathematical Modelling and Numerical Methods in Finance addresses the three most important aspects in the field: mathematical models, computational methods, and applications, and provides a solid overview of major new ideas and results in the three domains. - Coverage of all aspects of quantitative finance including models, computational methods and applications - Provides an overview of new ideas and results - Contributors are leaders of the field
Book Synopsis Methods of Mathematical Finance by : Ioannis Karatzas
Download or read book Methods of Mathematical Finance written by Ioannis Karatzas and published by Springer. This book was released on 2017-01-10 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This sequel to Brownian Motion and Stochastic Calculus by the same authors develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets, within the context of Brownian-motion-driven asset prices. The latter topic is extended to a study of equilibrium, providing conditions for existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the book. This book will be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options.
Book Synopsis Multi-Period Trading Via Convex Optimization by : Stephen Boyd
Download or read book Multi-Period Trading Via Convex Optimization written by Stephen Boyd and published by . This book was released on 2017-07-28 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph collects in one place the basic definitions, a careful description of the model, and discussion of how convex optimization can be used in multi-period trading, all in a common notation and framework.
Book Synopsis Seminar on Stochastic Analysis, Random Fields and Applications VII by : Robert C. Dalang
Download or read book Seminar on Stochastic Analysis, Random Fields and Applications VII written by Robert C. Dalang and published by Springer Science & Business Media. This book was released on 2013-09-05 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains refereed research or review articles presented at the 7th Seminar on Stochastic Analysis, Random Fields and Applications which took place at the Centro Stefano Franscini (Monte Verità) in Ascona , Switzerland, in May 2011. The seminar focused mainly on: - stochastic (partial) differential equations, especially with jump processes, construction of solutions and approximations - Malliavin calculus and Stein methods, and other techniques in stochastic analysis, especially chaos representations and convergence, and applications to models of interacting particle systems - stochastic methods in financial models, especially models for power markets or for risk analysis, empirical estimation and approximation, stochastic control and optimal pricing. The book will be a valuable resource for researchers in stochastic analysis and for professionals interested in stochastic methods in finance.
Book Synopsis Portfolio Choice Problems by : Nicolas Chapados
Download or read book Portfolio Choice Problems written by Nicolas Chapados and published by Springer Science & Business Media. This book was released on 2011-07-12 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
