Download or read book Optimal Investment with Transaction Costs and Stochastic Volatility Part II written by Maxim Bichuch and published by . This book was released on 2018 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this companion paper to “Optimal Investment with Transaction Costs and Stochastic Volatility Part I: Infinite Horizon”, "http://ssrn.com/abstract=2374150" http://ssrn.com/abstract=2374150, we give an accuracy proof for the finite time optimal investment and consumption problem under fast mean-reverting stochastic volatility of a joint asymptotic expansion in a time scale parameter and the small transaction cost. The supplemental appendix accompanies this paper is, available at "http://ssrn.com/abstract=3234374" http://ssrn.com/abstract=3234374, in which we prove the verification theorem that the value function is a viscosity solution of the HJB equation.

Download or read book Supplemental Appendix to Optimal Investment with Transaction Costs and Stochastic Volatility Part II written by Maxim Bichuch and published by . This book was released on 2018 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: This supplemental appendix accompanies "Optimal Investment with Transaction Costs and Stochastic Volatility Part II: Finite Horizon" by the same authors, available at:"http://ssrn.com/abstract=2659918" http://ssrn.com/abstract=2659918. In this appendix we prove the verification theorem that the value function is a viscosity solution of the HJB equation.

Download or read book Optimal Investment with Transaction Costs and Stochastic Volatility Part I written by Maxim Bichuch and published by . This book was released on 2015 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two major financial market complexities are transaction costs and uncertain volatility, and we analyze their joint impact on the problem of portfolio optimization. When volatility is constant, the transaction costs optimal investment problem has a long history, especially in the use of asymptotic approximations when the cost is small. Under stochastic volatility, but with no transaction costs, the Merton problem under general utility functions can also be analyzed with asymptotic methods. Here, we look at the long-run growth rate problem when both complexities are present, using separation of time scales approximations. This leads to perturbation analysis of an eigenvalue problem. We find the first term in the asymptotic expansion in the time scale parameter, of the optimal long-term growth rate, and of the optimal strategy, for fixed small transaction costs.The Companion piece for this paper are available at the following URL: "http://ssrn.com/abstract=2659918" http://ssrn.com/abstract=2659918.

Download or read book Should Stochastic Volatility Matter to the Cost Constrained Investor written by Scott M. Weiner and published by . This book was released on 2003 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: Significant strides have been made in the development of continuous-time portfolio optimization models since Merton (1969). Two independent advances have been the incorporation of transaction costs and time-varying volatility into the investor's optimization problem. Transaction costs generally inhibit investors from trading too often; they force the investor to choose between holding a suboptimal portfolio and reallocating the portfolio to the optimal allocation by incurring a fee. Several models, including Eastham and Hastings (1988) and Davis and Norman (1990), show that the investor can experience periods of passive investment (i.e., periods without transaction activity) as a result of transaction costs. Time-varying volatility, on the other hand, encourages trading activity, as it can result in an evolving optimal allocation of resources, as in Karatzas (1989). We examine the two-asset portfolio optimization problem when both elements are present. We show that the transaction cost framework in Korn (1998) can be extended to include a stochastic volatility process. We then specify a transaction cost model with stochastic volatility, based on Morton and Pliska (1995), and show that when the risk premium is linear in variance, the optimal strategy for the investor is independent of the level of volatility in the risky asset. We call this the Variance Invariance Principle.

Download or read book On Utility Based Investment Pricing and Hedging in Incomplete Markets written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis deals with rational investors who maximize their expected utility in incomplete markets. In Part I, we consider incompleteness induced by jumps and stochastic volatility. Using martingale methods we determine optimal investment strategies for power utility in a wide class of different models. Moreover, we show how first-order approximations of utility-based prices and hedging strategies can be computed by solving a quadratic hedging problem under a suitable measure. This representation result is then applied to affine models leading to semi-explicit solutions. In Part II, we deal with incompleteness due to proportional transaction costs. In finite discrete time we establish that there always exists a shadow price process, which lies within the bid-ask bounds of the original market with transaction costs and leads to the same maximal expected utility. We then show that this idea can also be used in actual computations. This is done by reconsidering the classical Merton problem with transaction costs and solving it by computing the shadow price and the optimal strategy simultaneously.

Download or read book Optimal Trading with Predictable Return and Stochastic Volatility written by Patrick Chan and published by . This book was released on 2015 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a class of dynamic portfolio optimization problems that allow for models of return predictability, transaction costs, and stochastic volatility. Determining the dynamic optimal portfolio in this general setting is almost always intractable. We propose a multiscale asymptotic expansion when the volatility process is characterized by its time scales of fluctuation. The analysis of the nonlinear Hamilton- Jacobi-Bellman PDE is a singular perturbation problem when volatility is fast mean-reverting; and it is a regular perturbation when the volatility is slowly varying. These analyses can be combined for multifactor multiscale stochastic volatility model. We present formal derivations of asymptotic approximations and demonstrate how the proposed algorithms improve our Profit & Loss using Monte Carlo simulations.

Download or read book The Effect of Stochastic Volatility on Portfolio Optimization with Transaction Costs written by Scott M. Weiner and published by . This book was released on 2000 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Optimal Investment written by L. C. G. Rogers and published by Springer Science & Business Media. This book was released on 2013-01-10 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: Readers of this book will learn how to solve a wide range of optimal investment problems arising in finance and economics. Starting from the fundamental Merton problem, many variants are presented and solved, often using numerical techniques that the book also covers. The final chapter assesses the relevance of many of the models in common use when applied to data.

Download or read book Multiscale Stochastic Volatility for Equity Interest Rate and Credit Derivatives written by Jean-Pierre Fouque and published by Cambridge University Press. This book was released on 2011-09-29 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM 'beta', and the Heston model and generalizations of it. 'Off-the-shelf' formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and applied mathematics.

Download or read book Optimal Investment and Consumption with Fixed and Proportional Transaction Costs written by Hong Liu and published by . This book was released on 2009 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the optimal investment and consumption policy for a constant absolute risk averse investor who faces fixed and/or proportional transaction costs when trading a stock and maximizes his expected utility from intertemporal consumption. We show that the Hamilton-Jacobi-Bellman PDE with free boundaries can be reduced to an ODE, which greatly simpli es the problem. Using the stochastic impulse and singular control techniques, we then derive the optimal investmment and consumption policy. In particular, when there are both fixed and proportional costs, it is shown that the optimal stock investment policy is to keep the dollar amount invested in the stock between two constant levels and upon reaching these two thresholds, the investor jumps to the corresponding optimal target level. We also provide detailed analysis of the optimal policy.

Download or read book Growth Optimal Investment with Transaction Costs written by Garud N. Iyengar and published by . This book was released on 1998 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Quantitative Fund Management written by M.A.H. Dempster and published by CRC Press. This book was released on 2008-12-22 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: The First Collection That Covers This Field at the Dynamic Strategic and One-Period Tactical Levels. Addressing the imbalance between research and practice, Quantitative Fund Management presents leading-edge theory and methods, along with their application in practical problems encountered in the fund management industry. A Current Snapshot of State-of-the-Art Applications of Dynamic Stochastic Optimization Techniques to Long-Term Financial Planning - The first part of the book initially looks at how the quantitative techniques of the equity industry are shifting from basic Markowitz mean-variance portfolio optimization to risk management and trading applications. This section also explores novel aspects of lifetime individual consumption investment problems, fixed-mix portfolio rebalancing allocation strategies, debt management for funding mortgages and national debt, and guaranteed return fund construction. Up-to-Date Overview of Tactical Financial Planning and Risk Management - The second section covers nontrivial computational approaches to tactical fund management. This part focuses on portfolio construction and risk management at the individual security or fund manager level over the period up to the next portfolio rebalance. It discusses non-Gaussian returns, new risk-return tradeoffs, and the robustness of benchmarks and portfolio decisions. The Future Use of Quantitative Techniques in Fund Management - With contributions from well-known academics and practitioners, this volume will undoubtedly foster the recognition and wider acceptance of stochastic optimization techniques in financial practice.

Download or read book A Shadow price Approach of the Problem of Optimal Investment consumption with Proportional Transaction Costs and Utilities of Power Type written by Jin Hyuk Choi and published by . This book was released on 2012 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: We revisit the optimal investment and consumption model of Davis and Norman (1990) and Shreve and Soner (1994), following a shadow-price approach similar to that of Kallsen and Muhle-Karbe (2010). Making use of the completeness of the model without transaction costs, we reformulate and reduce the Hamilton-Jacobi-Bellman equation for this singular stochastic control problem to a non-standard free-boundary problem for a first-order ODE with an integral constraint. Having shown that the free boundary problem has a smooth solution, we use it to construct the solution of the original optimal investment/consumption problem in a self-contained manner and without any recourse to the dynamic programming principle. By analyzing the properties of the free boundary problem, we provide an explicit characterization of model parameters for which the value function is finite. Furthermore, we prove that the value function, as well as the slopes of the lines demarcating the no-trading region, can be expanded as a series of integer powers of [lambda superscript 1/3]. The coefficients of arbitrary order in this expansion can be computed.

Download or read book Engineering Investment Process written by Florian Ielpo and published by Elsevier. This book was released on 2017-03-22 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineering Investment Process: Making Value Creation Repeatable explores the quantitative steps of a financial investment process. The authors study how these steps are articulated in order to make any value creation, whatever the asset class, consistent and robust. The discussion includes factors, portfolio allocation, statistical and economic backtesting, but also the influence of negative rates, dynamical trading, state-space models, stylized facts, liquidity issues, or data biases. Besides the quantitative concepts detailed here, the reader will find useful references to other works to develop an in-depth understanding of an investment process. - Blends academic research with practical experience from quants, fund managers, and economists - Puts financial mathematics and econometrics in their rightful place - Presents useful information that will increase the reader's understanding of markets - Clearly provides both the global framework, the investment process, and the useful econometric and financial tools that help in its construction - Includes efficient tools taken from up-to-date econometric and financial techniques

Download or read book Optimal Mean Reversion Trading written by Tim Leung (Professor of industrial engineering) and published by World Scientific. This book was released on 2015-11-26 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Optimal Mean Reversion Trading: Mathematical Analysis and Practical Applications provides a systematic study to the practical problem of optimal trading in the presence of mean-reverting price dynamics. It is self-contained and organized in its presentation, and provides rigorous mathematical analysis as well as computational methods for trading ETFs, options, futures on commodities or volatility indices, and credit risk derivatives. This book offers a unique financial engineering approach that combines novel analytical methodologies and applications to a wide array of real-world examples. It extracts the mathematical problems from various trading approaches and scenarios, but also addresses the practical aspects of trading problems, such as model estimation, risk premium, risk constraints, and transaction costs. The explanations in the book are detailed enough to capture the interest of the curious student or researcher, and complete enough to give the necessary background material for further exploration into the subject and related literature. This book will be a useful tool for anyone interested in financial engineering, particularly algorithmic trading and commodity trading, and would like to understand the mathematically optimal strategies in different market environments."--

Download or read book Stochastic Portfolio Theory written by E. Robert Fernholz and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic portfolio theory is a mathematical methodology for constructing stock portfolios and for analyzing the effects induced on the behavior of these portfolios by changes in the distribution of capital in the market. Stochastic portfolio theory has both theoretical and practical applications: as a theoretical tool it can be used to construct examples of theoretical portfolios with specified characteristics and to determine the distributional component of portfolio return. This book is an introduction to stochastic portfolio theory for investment professionals and for students of mathematical finance. Each chapter includes a number of problems of varying levels of difficulty and a brief summary of the principal results of the chapter, without proofs.

Download or read book Transaction Costs Trading Volume and the Liquidity Premium written by Stefan Gerhold and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a market with one safe and one risky asset, an investor with a long horizon, constant investment opportunities, and constant relative risk aversion trades with small proportional transaction costs. We derive explicit formulas for the optimal investment policy, its implied welfare, liquidity premium, and trading volume. At the first order, the liquidity premium equals the spread, times share turnover, times a universal constant. Results are robust to consumption and finite-horizons. We exploit the equivalence of the transaction cost market to another frictionless market, with a shadow risky asset, in which investment opportunities are stochastic. The shadow price is also found explicitly.