Download or read book Numerical Solution of Dynamic Portfolio Optimization with Transaction Costs written by Yongyang Cai and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We apply numerical dynamic programming to multi-asset dynamic portfolio optimization problems with proportional transaction costs. Examples include problems with one safe asset plus two to six risky stocks, and seven to 360 trading periods in a finite horizon problem. These examples show that it is now tractable to solve such problems.

Download or read book Dynamic Portfolio Optimization with Transaction Costs and State Dependent Drift written by Jan Palczewski and published by . This book was released on 2014 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present an efficient numerical method to determine optimal portfolio strategies under time- and state-dependent drift and proportional transaction costs. This scenario arises when investors have behavioral biases or the actual drift is unknown and needs to be estimated. The numerical method solves dynamic optimal portfolio problems for time-horizons of up to 40 years. It is applied to measure the value of information and the loss from transaction costs using the indifference principle.

Download or read book Numerical Solution of Dinamic Portfolio Optimization with Transaction Costs written by Yongyang Cai and published by . This book was released on 2013 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Dynamic Portfolio Optimization with Liquidity Cost and Market Impact written by Rongju Zhang and published by . This book was released on 2018 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a simulation-and-regression method for solving dynamic portfolio optimization problems in the presence of general transaction costs, liquidity costs and market impact. This method extends the classical least squares Monte Carlo algorithm to incorporate switching costs, corresponding to transaction costs and transient liquidity costs, as well as multiple endogenous state variables, namely the portfolio value and the asset prices subject to permanent market impact. To handle endogenous state variables, we adapt a control randomization approach to portfolio optimization problems and further improve the numerical accuracy of this technique for the case of discrete controls. We validate our modified numerical method by solving a realistic cash-and-stock portfolio with a power-law liquidity model. We identify the certainty equivalent losses associated with ignoring liquidity effects, and illustrate how our dynamic optimization method protects the investor's capital under illiquid market conditions. Lastly, we analyze, under different liquidity conditions, the sensitivities of certainty equivalent returns and optimal allocations with respect to trading volume, stock price volatility, initial investment amount, risk aversion level and investment horizon.

Download or read book Modeling and Numerical Solution of Portfolio Optimization Problems with Transaction Costs An Option Pricing Approach written by Zhen Liu and published by . This book was released on 2007 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: Portfolio optimization problems with transaction costs have been widely studied by both financial economists and financial engineers through various approaches. In this paper, we propose the following approach. In analogy to American option pricing, we study the problem through the Finite Element Method (FEM) combined with an optimization method: We set up a buy-and-hold problem and then we find an optimal set of trades to move to an optimal portfolio whenever the current portfolio is far from the ideal. Local Discontinuous Galerkin (LDG) FEM is used to solve the partial differential equation (PDE) associated with the buy-and-hold problem. Coupled with the Runge-Kutta method for time discretization, this method is local with respect to spatial variable, can be used to achieve any order of accuracy and is explicit in the semi-discrete Ordinary Differential Equation (ODE) form. Also it is amendable to parallel computing. In this paper we give error bounds for the LDG method, with which we establish overall bounds for the portfolio optimization problem and prove the convergence of this method.

Download or read book Dynamic Portfolio Choice with Linear Rebalancing Rules written by Ciamac C. Moallemi and published by . This book was released on 2015 with total page 59 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a broad class of dynamic portfolio optimization problems that allow for complex models of return predictability, transaction costs, trading constraints, and risk considerations. Determining an optimal policy in this general setting is almost always intractable. We propose a class of linear rebalancing rules, and describe an efficient computational procedure to optimize with this class. We illustrate this method in the context of portfolio execution, and show that it achieves near optimal performance. We consider another numerical example involving dynamic trading with mean-variance preferences and demonstrate that our method can result in economically large benefits.

Download or read book Simulation Based Portfolio Optimization for Large Portfolios with Transaction Costs written by Kumar Muthuraman and published by . This book was released on 2005 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a portfolio optimization problem where the investor's objective is to maximize the long-term expected growth rate, in the presence of proportional transaction costs. This problem belongs to the class of stochastic control problems with singular controls, which are usually solved by computing solutions to related partial differential equations called the free-boundary Hamilton Jacobi Bellman (HJB) equations. The dimensionality of the HJB equals the number of stocks in the portfolio. The runtime of existing solution methods grow super-exponentially with dimension, making them unsuitable to compute optimal solutions to portfolio optimization problems with even four stocks. In this work we first present a boundary update procedure that converts the free boundary problem into a sequence of fixed boundary problems. Then by combining simulation with the boundary update procedure, we provide a computational scheme whose runtime, as shown by the numerical tests, scales polynomially in dimension. The results are compared and corroborated against existing methods that scale super-exponentially in dimension. The method presented herein enables the first ever computational solution to free-boundary problems in dimensions greater than three.

Download or read book Strategic Asset Allocation written by John Y. Campbell and published by OUP Oxford. This book was released on 2002-01-03 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Academic finance has had a remarkable impact on many financial services. Yet long-term investors have received curiously little guidance from academic financial economists. Mean-variance analysis, developed almost fifty years ago, has provided a basic paradigm for portfolio choice. This approach usefully emphasizes the ability of diversification to reduce risk, but it ignores several critically important factors. Most notably, the analysis is static; it assumes that investors care only about risks to wealth one period ahead. However, many investors—-both individuals and institutions such as charitable foundations or universities—-seek to finance a stream of consumption over a long lifetime. In addition, mean-variance analysis treats financial wealth in isolation from income. Long-term investors typically receive a stream of income and use it, along with financial wealth, to support their consumption. At the theoretical level, it is well understood that the solution to a long-term portfolio choice problem can be very different from the solution to a short-term problem. Long-term investors care about intertemporal shocks to investment opportunities and labor income as well as shocks to wealth itself, and they may use financial assets to hedge their intertemporal risks. This should be important in practice because there is a great deal of empirical evidence that investment opportunities—-both interest rates and risk premia on bonds and stocks—-vary through time. Yet this insight has had little influence on investment practice because it is hard to solve for optimal portfolios in intertemporal models. This book seeks to develop the intertemporal approach into an empirical paradigm that can compete with the standard mean-variance analysis. The book shows that long-term inflation-indexed bonds are the riskless asset for long-term investors, it explains the conditions under which stocks are safer assets for long-term than for short-term investors, and it shows how labor income influences portfolio choice. These results shed new light on the rules of thumb used by financial planners. The book explains recent advances in both analytical and numerical methods, and shows how they can be used to understand the portfolio choice problems of long-term investors.

Download or read book Handbook of Computational Economics written by Karl Schmedders and published by Newnes. This book was released on 2013-12-31 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Computational Economics summarizes recent advances in economic thought, revealing some of the potential offered by modern computational methods. With computational power increasing in hardware and algorithms, many economists are closing the gap between economic practice and the frontiers of computational mathematics. In their efforts to accelerate the incorporation of computational power into mainstream research, contributors to this volume update the improvements in algorithms that have sharpened econometric tools, solution methods for dynamic optimization and equilibrium models, and applications to public finance, macroeconomics, and auctions. They also cover the switch to massive parallelism in the creation of more powerful computers, with advances in the development of high-power and high-throughput computing. Much more can be done to expand the value of computational modeling in economics. In conjunction with volume one (1996) and volume two (2006), this volume offers a remarkable picture of the recent development of economics as a science as well as an exciting preview of its future potential. - Samples different styles and approaches, reflecting the breadth of computational economics as practiced today - Focuses on problems with few well-developed solutions in the literature of other disciplines - Emphasizes the potential for increasing the value of computational modeling in economics

Download or read book Local Discontinuous Galerkin Method for Portfolio Optimization with Transaction Costs written by John R. Birge and published by . This book was released on 2015 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the continuous time portfolio selection problem over a finite horizon for an investor who maximizes the expected utility of terminal wealth and faces transaction costs. The portfolio consists of a risk-free asset, and a risky asset whose price is modeled as a geometric Brownian motion. The problem can be formulated as a stochastic singular control or an impulse control problem depending on whether the transaction costs are of proportional or fixed type. Due to the intractability of the problem, modelers resort to numerical methods to obtain approximations of solutions to the problem. In this paper we propose a stable and high-order computational scheme to solve this problem, which is capable of handling any form of transaction costs. Specifically, we implement the Local Discontinuous Galerkin (LDG) Finite Element Method (FEM) to solve the resulting convection-diffusion Partial Differential Equation (PDE), and obtain error estimates for the LDG method. Moreover, we prove the convergence of the scheme. Our numerical experiments show the order of accuracy of the LDG method and illustrate the optimal policies under various kinds of transaction costs.

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.

Download or read book Portfolio Selection with Transaction Costs and Jump Diffusion Asset Dynamics I written by Michal Czerwonko and published by . This book was released on 2017 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive allocation rules under isoelastic utility for a mixed jump-diffusion process in a two-asset portfolio selection problem with finite horizon in the presence of proportional transaction costs. We adopt a discrete time formulation, let the number of periods go to infinity, and show that it converges efficiently to the continuous time solution for the cases where this solution is known. We then apply this discretization to derive numerically the boundaries of the region of no transactions. Our discrete-time numerical approach outperforms alternative continuous-time approximations of the problem.

Download or read book Dynamic Portfolio Theory and Management written by Richard E. Oberuc and published by McGraw Hill Professional. This book was released on 2004 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description

Download or read book Difference Equations Discrete Dynamical Systems and Applications written by Martin Bohner and published by Springer. This book was released on 2015-12-01 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings of the 20th International Conference on Difference Equations and Applications cover the areas of difference equations, discrete dynamical systems, fractal geometry, difference equations and biomedical models, and discrete models in the natural sciences, social sciences and engineering. The conference was held at the Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences (Hubei, China), under the auspices of the International Society of Difference Equations (ISDE) in July 2014. Its purpose was to bring together renowned researchers working actively in the respective fields, to discuss the latest developments, and to promote international cooperation on the theory and applications of difference equations. This book will appeal to researchers and scientists working in the fields of difference equations, discrete dynamical systems and their applications.

Download or read book Multi Dimensional Portfolio Optimization with Proportional Transaction Costs written by Kumar Muthuraman and published by . This book was released on 2004 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: We provide a computational study of the problem of optimally allocating wealth among multiple stocks and a bank account, in order to maximize the infinite horizon discounted utility of consumption. We consider the situation where the transfer of wealth from one asset to another involves transaction costs that are proportional to the amount of wealth transferred. Our model allows for correlation between the price processes, which in turn gives rise to interesting hedging strategies. This results in a stochastic control problem with both drift-rate and singular controls, that can be recast as a free boundary problem in partial differential equations. Adapting the finite element method and using an iterative procedure that converts the free-boundary problem into a sequence of fixed boundary problems, we provide an efficient numerical method for solving this problem. We present computational results that describe the impact of volatility, risk aversion of the investor, level of transaction costs and correlation among the risky assets on the structure of the optimal policy. Finally we suggest and quantify some heuristic approximations.

Download or read book Iaeng Transactions On Engineering Sciences Special Issue For The International Association Of Engineers Conferences 2014 written by Sio-iong Ao and published by World Scientific. This book was released on 2015-03-11 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two large international conferences on Advances in Engineering Sciences were held in Hong Kong, March 12-14, 2014, under the International MultiConference of Engineers and Computer Scientists (IMECS 2014), and in London, UK, 2-4 July, 2014, under the World Congress on Engineering 2014 (WCE 2014) respectively. This volume contains 37 revised and extended research articles written by prominent researchers participating in the conferences. Topics covered include engineering mathematics, computer science, electrical engineering, manufacturing engineering, industrial engineering, and industrial applications. The book offers tremendous state-of-the-art advances in engineering sciences and also serves as an excellent reference work for researchers and graduate students working with/on engineering sciences.

Download or read book Worst Case Portfolio Optimization with Proportional Transaction Costs written by Christoph Belak and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We study optimal asset allocation in a crash-threatened financial market with proportional transaction costs. The market is assumed to be in either a normal state, in which the risky asset follows a geometric Brownian motion, or in a crash state, in which the price of the risky asset can suddenly drop by a certain relative amount. We only assume the maximum number and the maximum relative size of the crashes to be given and do not make any assumptions about their distributions. For every investment strategy, we identify the worst-case scenario in the sense that the expected utility of terminal wealth is minimized. The objective is then to determine the investment strategy which yields the highest expected utility in its worst-case scenario.We solve the problem for utility functions with constant relative risk aversion using a stochastic control approach. We characterize the value function as the unique viscosity solution of a second-order nonlinear partial differential equation. The optimal strategies are characterized by time-dependent free boundaries which we compute numerically. The numerical examples suggest that it is not optimal to invest any wealth in the risky asset close to the investment horizon, while a long position in the risky asset is optimal if the remaining investment period is sufficiently large.