Download or read book Worst Case Approach to Strategic Optimal Portfolio Selection Under Transaction Costs and Trading Limits written by Nikolay Andreev and published by . This book was released on 2016 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study a worst-case scenario approach to the stochastic dynamic programming problem, presenting a general probability-based framework and some properties of the arising Bellman-Isaacs equation which allow to obtain a closed-form analytic solution. We also adapt the results for a discrete financial market and the problem of strategic portfolio selection in the presence of transaction costs and trading limits with unspecified stochastic process of market parameters. Unlike the classic stochastic programming, the approach is model-free while the solution can be easily found numerically under economically reasonable assumptions. All results hold for a general class of utility functions and several risky assets. For a special case of proportional transaction costs and CRRA utility, we present a numerical scheme which allows to reduce the dimensionality of the Bellman-Isaacs equation by a number of risky assets.

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.

Download or read book Optimal Portfolio Selection with Transaction Costs and Event Risk written by Hong Liu and published by . This book was released on 2009 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: Models with event risk (the possibility of sudden large price movements) have proven important for option pricing (e.g., Bates (1996))and optimal portfolio selection (e.g., Liu, Longstaff and Pan(2003)). However, most of the existing studies ignore transaction costs which are prevalent in almost all of the financial markets. How investors should trade in the presence of event risks and transaction costs remains an important but unanswered question. In this paper, we consider the optimal trading strategy for a CRRA investor who derives utility from terminal wealth and can continuously trade in a riskless asset and a risky asset. The risky asset, whose price follows a jump diffusion, is subject to proportional transaction costs. We show that the optimal trading strategy is to maintain the fraction of wealth invested in the risky asset between two bounds. In contrast to the case without jump risk, this fraction can jump outside the bounds which implies a discrete transaction back to the closest boundary and thus a greater transaction cost payment. We characterize the value function and provide bounds on the trading boundaries. Somewhat surprisingly, we find that an increase in transaction costs may increase trading frequency. Our numerical results suggest that event risk significantly reduces stock holdings and decreases trading frequency. We also show that the boundaries are affected not only by jump sizes but also by the uncertainty about jump sizes. Furthermore, we examine how the optimal transaction boundaries vary through time for investors with deterministic horizons.

Download or read book Optimal Portfolio Selection with Fixed Transaction Costs in the Presence of Jumps and Random Drift written by Ajay Subramanian Aiyer and published by . This book was released on 1996 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Optimal Portfolios written by Ralf Korn and published by World Scientific. This book was released on 1997 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of the book is the construction of optimal investment strategies in a security market model where the prices follow diffusion processes. It begins by presenting the complete Black-Scholes type model and then moves on to incomplete models and models including constraints and transaction costs. The models and methods presented will include the stochastic control method of Merton, the martingale method of Cox-Huang and Karatzas et al., the log optimal method of Cover and Jamshidian, the value-preserving model of Hellwig etc.

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 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 Optimal Portfolio Choice Under Partial Information and Transaction Costs written by Huamao Wang and published by . This book was released on 2010 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop and analyze a model of optimal portfolio choice with a finite time horizon T. The investor's objective is to maximize the expected utility of termi- nal wealth based on partial information generated by stock prices. Rebalancing the portfolio composed of a stock and a bank account incurs transaction costs. This thesis extends the literature by examining the joint impact of partial in- formation and transaction costs on investors' decisions and expected utilities. After estimating the uncertain drift from historical prices, an investor up- dates the estimate over [0, T] based on partial information. This investor learns about the drift with the Kalman-Bucy filter, which provides a statistically op- timal estimate. Three regions of the state space with two free boundaries char- acterize the optimal portfolio strategy. A numerical algorithm using dynamic programming and a Markov chain approximation solves the model. The ex- isting algorithm with known parameters is time consuming and liable to cause underflow or overflow of the range of values represented. We propose four im- provements to overcome the drawbacks. The algorithm with modifications can be applied to the model under partial information according to the separation principle. We define two measures to quantify the losses in utility caused by partial information and transaction costs. Four quantities are introduced to describe investors' trading behaviours. With simulations of stock prices and the drift, the comparative analysis of five market parameters reveals the properties of the model and tests the robustness of the algorithm. Compared with the investors who use erroneous estimates of the drift, the learning investor's portfolio hold- ings are close to the informed investor's portfolio holdings. The average cost per transaction to the learning investor is the lowest. This investor has these benefits because the filter reduces uncertainty. We discuss the implications for practitioners to highlight the practical contributions of this research. KEY WORDS: investment; portfolio choice; parameter uncertainty; transaction costs; dynamic programming.

Download or read book Online Portfolio Selection written by Bin Li and published by CRC Press. This book was released on 2018-10-30 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the aim to sequentially determine optimal allocations across a set of assets, Online Portfolio Selection (OLPS) has significantly reshaped the financial investment landscape. Online Portfolio Selection: Principles and Algorithms supplies a comprehensive survey of existing OLPS principles and presents a collection of innovative strategies that leverage machine learning techniques for financial investment. The book presents four new algorithms based on machine learning techniques that were designed by the authors, as well as a new back-test system they developed for evaluating trading strategy effectiveness. The book uses simulations with real market data to illustrate the trading strategies in action and to provide readers with the confidence to deploy the strategies themselves. The book is presented in five sections that: Introduce OLPS and formulate OLPS as a sequential decision task Present key OLPS principles, including benchmarks, follow the winner, follow the loser, pattern matching, and meta-learning Detail four innovative OLPS algorithms based on cutting-edge machine learning techniques Provide a toolbox for evaluating the OLPS algorithms and present empirical studies comparing the proposed algorithms with the state of the art Investigate possible future directions Complete with a back-test system that uses historical data to evaluate the performance of trading strategies, as well as MATLAB® code for the back-test systems, this book is an ideal resource for graduate students in finance, computer science, and statistics. It is also suitable for researchers and engineers interested in computational investment. Readers are encouraged to visit the authors’ website for updates: http://olps.stevenhoi.org.

Download or read book Penalty Methods for Continuous Time Portfolio Selection with Proportional Transaction Costs written by Min Dai and published by . This book was released on 2008 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: We are concerned with numerical solutions for the continuous-time portfolio selection with proportional transaction costs which is described as a singular stochastic control problem. The associated value function is governed by a variational inequality with gradient constraints. We propose a penalty method to deal with the gradient constraints and employ the finite difference discretization. Convergence analysis is presented. We also show that the standard penalty method can be applied in the case of single risky asset where the problem can be reduced to a standard variational inequality. Numerical results are given to demonstrate the efficiency of the methods and to examine the behaviors of the optimal trading strategy.

Download or read book Portfolio Optimization with Concave Transaction Costs written by and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Optimal Portfolio Selection with Transaction Costs written by Phelim P. Boyle and published by . This book was released on 1994 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Worst Case Portfolio Optimization Transaction Costs and Bubbles written by Christoph Belak and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Financial Derivatives Pricing Selected Works Of Robert Jarrow written by Robert A Jarrow and published by World Scientific. This book was released on 2008-10-08 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of original papers by Robert Jarrow that contributed to significant advances in financial economics. Divided into three parts, Part I concerns option pricing theory and its foundations. The papers here deal with the famous Black-Scholes-Merton model, characterizations of the American put option, and the first applications of arbitrage pricing theory to market manipulation and liquidity risk.Part II relates to pricing derivatives under stochastic interest rates. Included is the paper introducing the famous Heath-Jarrow-Morton (HJM) model, together with papers on topics like the characterization of the difference between forward and futures prices, the forward price martingale measure, and applications of the HJM model to foreign currencies and commodities.Part III deals with the pricing of financial derivatives considering both stochastic interest rates and the likelihood of default. Papers cover the reduced form credit risk model, in particular the original Jarrow and Turnbull model, the Markov model for credit rating transitions, counterparty risk, and diversifiable default risk.

Download or read book A Simple Algorithm for Optimal Portfolio Selection with Fixed Transaction Costs written by Nitin Ratilal Patel and published by . This book was released on 1979 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Unified Approach to Portfolio Optimization with Linear Transaction Costs written by Valeriy Zakamulin and published by . This book was released on 2010 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we study the continuous time optimal portfolio selection problem for an investor with a finite horizon who maximizes expected utility of terminal wealth and faces transaction costs in the capital market. It is well known that, depending on a particular structure of transaction costs, such a problem is formulated and solved within either stochastic singular control or stochastic impulse control framework. In this paper we propose a unified framework, which generalizes the contemporary approaches and is capable to deal with any problem where transaction costs are a linear/piecewise-linear function of the volume of trade. We also discuss some methods for solving numerically the problem within our unified framework.

Download or read book On line Portfolio Selection Strategy with Prediction in the Presence of Transaction Costs written by Matthew Lloyd Tucker and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: