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Multi Period Portfolio Optimization Model With Cone Constraints And Discrete Decisions
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Book Synopsis Multi-Period Portfolio Optimization Model with Cone Constraints and Discrete Decisions by : Ümit Saglam
Download or read book Multi-Period Portfolio Optimization Model with Cone Constraints and Discrete Decisions written by Ümit Saglam and published by . This book was released on 2019 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this study, we consider multi-period portfolio optimization model that is formulated as a mixed-integer second-order cone programming problems (MISOCPs). The Markowitz (1952) mean/variance framework has been extended by including transaction costs, conditional value-at-risk (CVaR), diversification-by-sector and buy-in thresholds constraints. The model is obtained using a binary scenario tree that is constructed with monthly returns of the stocks from the S&P 500. We solve these models with a MATLAB based Mixed Integer Linear and Nonlinear Optimizer (MILANO). Numerical results show that we can solve small to medium-sized instances successfully, and we provide a substantial improvement in runtimes using warmstarts in outer approximation algorithm.
Book Synopsis Single- and Multi-Period Portfolio Optimization with Cone Constraints and Discrete Decisions by : Ümit Saglam
Download or read book Single- and Multi-Period Portfolio Optimization with Cone Constraints and Discrete Decisions written by Ümit Saglam and published by . This book was released on 2019 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Portfolio optimization literature has come quite far in the decades since the first publication, and many modern models are formulated using second-order cone constraints and take discrete decisions into consideration. In this study, we consider both single-period and multi-period portfolio optimization problems based on the Markowitz (1952) mean/variance framework, where there is a trade-off between expected return and the risk that the investor may be willing to take on. Our model is aggregated from current literature. In this model, we have included transaction costs, conditional value-at-risk (CVaR) constraints, diversification-by-sector constraints, and buy-in-thresholds. Our numerical experiments are conducted on portfolios drawn from 20 to 400 different stocks available from the S&P 500 for the single period-model. The multi-period portfolio optimization model is obtained using a binary scenario tree that is constructed with monthly returns of the closing price of the stocks from the S&P 500. We solve these models with a MATLAB based Mixed Integer Linear and Nonlinear Optimizer (MILANO). We provide a substantial improvement in runtimes using warmstarts in both branch-and-bound and outer approximation algorithms.
Book Synopsis Advanced Optimization and Statistical Methods in Portfolio Optimization and Supply Chain Management by : Ümit Să̆glam
Download or read book Advanced Optimization and Statistical Methods in Portfolio Optimization and Supply Chain Management written by Ümit Să̆glam and published by . This book was released on 2014 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is on advanced mathematical programming with applications in portfolio optimization and supply chain management. Specifically, this research started with modeling and solving large and complex optimization problems with cone constraints and discrete variables, and then expanded to include problems with multiple decision perspectives and nonlinear behavior. The original work and its extensions are motivated by real world business problems. The first contribution of this dissertation, is to algorithmic work for mixed-integer second-order cone programming problems (MISOCPs), which is of new interest to the research community. This dissertation is among the first ones in the field and seeks to develop a robust and effective approach to solving these problems. There is a variety of important application areas of this class of problems ranging from network reliability to data mining, and from finance to operations management. This dissertation also contributes to three applications that require the solution of complex optimization problems. The first two applications arise in portfolio optimization, and the third application is from supply chain management. In our first study, we consider both single- and multi-period portfolio optimization problems based on the Markowitz (1952) mean/variance framework. We have also included transaction costs, conditional value-at-risk (CVaR) constraints, and diversification constraints to approach more realistic scenarios that an investor should take into account when he is constructing his portfolio. Our second work proposes the empirical validation of posing the portfolio selection problem as a Bayesian decision problem dependent on mean, variance and skewness of future returns by comparing it with traditional mean/variance efficient portfolios. The last work seeks supply chain coordination under multi-product batch production and truck shipment scheduling under different shipping policies. These works present a thorough study of the following research foci: modeling and solution of large and complex optimization problems, and their applications in supply chain management and portfolio optimization.
Book Synopsis Performance Bounds and Suboptimal Policies for Multi-period Investment by : Stephen P. Boyd
Download or read book Performance Bounds and Suboptimal Policies for Multi-period Investment written by Stephen P. Boyd and published by . This book was released on 2014 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider dynamic trading of a portfolio of assets in discrete periods over a finite time horizon, with arbitrary time-varying distribution of asset returns. The goal is to maximize the total expected revenue from the portfolio, while respecting constraints on the portfolio such as a required terminal portfolio and leverage and risk limits. The revenue takes into account the gross cash generated in trades, transaction costs, and costs associated with the positions, such as fees for holding short positions. Our model has the form of a stochastic control problem with linear dynamics and convex cost function and constraints. While this problem can be tractably solved in several special cases, such as when all costs are convex quadratic, or when there are no transaction costs, our focus is on the more general case, with nonquadratic cost terms and transaction costs. We show how to use linear matrix inequality techniques and semidefinite programming to produce a quadratic bound on the value function, which in turn gives a bound on the optimal performance. This performance bound can be used to judge the performance obtained by any suboptimal policy. As a by-product of the performance bound computation, we obtain an approximate dynamic programming policy that requires the solution of a convex optimization problem, often a quadratic program, to determine the trades to carry out in each step. While we have no theoretical guarantee that the performance of our suboptimal policy is always near the performance bound (which would imply that it is nearly optimal) we observe that in numerical examples the two values are typically close.
Book Synopsis Multi-period Scenario Generation to Support Portfolio Optimization by : Erhan Deniz
Download or read book Multi-period Scenario Generation to Support Portfolio Optimization written by Erhan Deniz and published by . This book was released on 2009 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Programming (SP) models are widely used for real life problems involving uncertainty. The random nature of problem parameters is modeled via discrete scenarios, which makes the scenario generation process very critical to the success of the overall approach. In this study we consider a portfolio management problem and propose two scenario generation algorithms and a SP model to support investment decisions. The main objective of the scenario generation algorithms is to infer representative probability values to be assigned to the scenario realizations sampled from historical data. The first algorithm assigns the probabilities by using similarity scores, assigning higher probabilities to the scenarios with data paths that are relatively similar to historical paths, where similarity scores are computed by means of distance measures. We first implement this approach using the weighted Euclidean distance (WED). We also propose a new distance measure to obtain similarity scores as an alternative to WED. The second scenario generation algorithm is based on the combination of moment-matching technique and the Exponential Generalized Auto-Regressive Conditional Heteroskedasticity (EGARCH) model. Scenario probabilities are assigned such that the first four moments of the sampled returns are fit to target moments through a linear programming model, where the second target moments are set to be conditional on the past scenarios on the scenario tree using the EGARCH model. An additional set of constraints are proposed to increase robustness. The generated scenarios become input to the SP model to restructure the existing portfolio such that the expected final wealth is maximized and the risk exposure is controlled through constraining Conditional Value-at-Risk at each decision epoch on the scenario tree. We finally propose a generic approach to reduce potential losses and implement it on a logistic regression framework.
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 Multi-period portfolio optimization by : Heiko Siede
Download or read book Multi-period portfolio optimization written by Heiko Siede and published by . This book was released on 2000 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Stochastic Programming by : John R. Birge
Download or read book Introduction to Stochastic Programming written by John R. Birge and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This rapidly developing field encompasses many disciplines including operations research, mathematics, and probability. Conversely, it is being applied in a wide variety of subjects ranging from agriculture to financial planning and from industrial engineering to computer networks. This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability. The authors present a broad overview of the main themes and methods of the subject, thus helping students develop an intuition for how to model uncertainty into mathematical problems, what uncertainty changes bring to the decision process, and what techniques help to manage uncertainty in solving the problems. The early chapters introduce some worked examples of stochastic programming, demonstrate how a stochastic model is formally built, develop the properties of stochastic programs and the basic solution techniques used to solve them. The book then goes on to cover approximation and sampling techniques and is rounded off by an in-depth case study. A well-paced and wide-ranging introduction to this subject.
Book Synopsis Multi-period Portfolio Optimization in the Presence of Transaction Costs by : Husnu Kipeak
Download or read book Multi-period Portfolio Optimization in the Presence of Transaction Costs written by Husnu Kipeak and published by . This book was released on 2001 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Minimax Approaches to Robust Model Predictive Control by : Johan Löfberg
Download or read book Minimax Approaches to Robust Model Predictive Control written by Johan Löfberg and published by Linköping University Electronic Press. This book was released on 2003-04-11 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Controlling a system with control and state constraints is one of the most important problems in control theory, but also one of the most challenging. Another important but just as demanding topic is robustness against uncertainties in a controlled system. One of the most successful approaches, both in theory and practice, to control constrained systems is model predictive control (MPC). The basic idea in MPC is to repeatedly solve optimization problems on-line to find an optimal input to the controlled system. In recent years, much effort has been spent to incorporate the robustness problem into this framework. The main part of the thesis revolves around minimax formulations of MPC for uncertain constrained linear discrete-time systems. A minimax strategy in MPC means that worst-case performance with respect to uncertainties is optimized. Unfortunately, many minimax MPC formulations yield intractable optimization problems with exponential complexity. Minimax algorithms for a number of uncertainty models are derived in the thesis. These include systems with bounded external additive disturbances, systems with uncertain gain, and systems described with linear fractional transformations. The central theme in the different algorithms is semidefinite relaxations. This means that the minimax problems are written as uncertain semidefinite programs, and then conservatively approximated using robust optimization theory. The result is an optimization problem with polynomial complexity. The use of semidefinite relaxations enables a framework that allows extensions of the basic algorithms, such as joint minimax control and estimation, and approx- imation of closed-loop minimax MPC using a convex programming framework. Additional topics include development of an efficient optimization algorithm to solve the resulting semidefinite programs and connections between deterministic minimax MPC and stochastic risk-sensitive control. The remaining part of the thesis is devoted to stability issues in MPC for continuous-time nonlinear unconstrained systems. While stability of MPC for un-constrained linear systems essentially is solved with the linear quadratic controller, no such simple solution exists in the nonlinear case. It is shown how tools from modern nonlinear control theory can be used to synthesize finite horizon MPC controllers with guaranteed stability, and more importantly, how some of the tech- nical assumptions in the literature can be dispensed with by using a slightly more complex controller.
Book Synopsis A Geometric Approach to Multiperiod Mean Variance Optimization of Assets and Liabilities by :
Download or read book A Geometric Approach to Multiperiod Mean Variance Optimization of Assets and Liabilities written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a geometric approach to discrete time multiperiod mean variance portfolio optimization that largely simplifies the mathematical analysis and the economic interpretation of such model settings. We show that multiperiod mean variance optimal policies can be decomposed in an orthogonal set of basis strategies, each having a clear economic interpretation. This implies that the corresponding multi period mean variance frontiers are spanned by an orthogonal basis of dynamic returns. Specifically, in a k-period model the optimal strategy is a linear combination of a single k-period global minimum second moment strategy and a sequence of k local excess return strategies which expose the dynamic portfolio optimally to each single-period asset excess return. This decomposition is a multi period version of Hansen and Richard (1987) orthogonal representation of single-period mean variance frontiers and naturally extends the basic economic intuition of the static Markowitz model to the multiperiod context. Using the geometric approach to dynamic mean variance optimization we obtain closed form solutions in the i.i.d. setting for portfolios consisting of both assets and liabilities (AL), each modelled by a distinct state variable. As a special case, the solution of the mean variance problem for the asset only case in Li and Ng (2000) follows directly and can be represented in terms of simple products of some single period orthogonal returns. We illustrate the usefulness of our geometric representation of multi-periods optimal policies and mean variance frontiers by discussing specific issued related to AL portfolios: The impact of taking liabilities into account on the implied mean variance frontiers, the quantification of the impact of the investment horizon and the determination of the optimal initial funding ratio.
Book Synopsis A Geometric Approach to Multiperiod Mean Variance Optimization of Assets and Liabilities by : Markus Leippold
Download or read book A Geometric Approach to Multiperiod Mean Variance Optimization of Assets and Liabilities written by Markus Leippold and published by . This book was released on 2002 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Max Plus at Work by : Bernd Heidergott
Download or read book Max Plus at Work written by Bernd Heidergott and published by Princeton University Press. This book was released on 2014-09-08 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Trains pull into a railroad station and must wait for each other before leaving again in order to let passengers change trains. How do mathematicians then calculate a railroad timetable that accurately reflects their comings and goings? One approach is to use max-plus algebra, a framework used to model Discrete Event Systems, which are well suited to describe the ordering and timing of events. This is the first textbook on max-plus algebra, providing a concise and self-contained introduction to the topic. Applications of max-plus algebra abound in the world around us. Traffic systems, computer communication systems, production lines, and flows in networks are all based on discrete even systems, and thus can be conveniently described and analyzed by means of max-plus algebra. The book consists of an introduction and thirteen chapters in three parts. Part One explores the introduction of max-plus algebra and of system descriptions based upon it. Part Two deals with a real application, namely the design of timetables for railway networks. Part Three examines various extensions, such as stochastic systems and min-max-plus systems. The text is suitable for last-year undergraduates in mathematics, and each chapter provides exercises, notes, and a reference section.
Book Synopsis Multi-period Trading Via Convex Optimization by : Stephen P. Boyd
Download or read book Multi-period Trading Via Convex Optimization written by Stephen P. Boyd and published by . This book was released on 2017 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a basic model of multi-period trading, which can be used to evaluate the performance of a trading strategy. We describe a framework for single-period optimization, where the trades in each period are found by solving a convex optimization problem that trades off expected return, risk, transaction cost and holding cost such as the borrowing cost for shorting assets. We then describe a multi-period version of the trading method, where optimization is used to plan a sequence of trades, with only the first one executed, using estimates of future quantities that are unknown when the trades are chosen. The single period method traces back to Markowitz; the multi-period methods trace back to model predictive control. Our contribution is to describe the single-period and multi-period methods in one simple framework, giving a clear description of the development and the approximations made. In this paper, we do not address a critical component in a trading algorithm, the predictions or forecasts of future quantities. The methods we describe in this paper can be thought of as good ways to exploit predictions, no matter how they are made. We have also developed a companion open-source software library that implements many of the ideas and methods described in the paper.
Book Synopsis Multi-period Portfolio Optimization by : Jules Clement Mba
Download or read book Multi-period Portfolio Optimization written by Jules Clement Mba and published by . This book was released on 2019 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Convex Optimization by : Stephen P. Boyd
Download or read book Convex Optimization written by Stephen P. Boyd and published by Cambridge University Press. This book was released on 2004-03-08 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
