Download or read book Portfolio Optimization with Stochastic Dividends and Stochastic Volatility written by Katherine Yvonne Varga and published by . This book was released on 2015 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Portfolio Optimization Stochastic Volatility Asymptotics written by Jean-Pierre Fouque and published by . This book was released on 2015 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the Merton portfolio optimization problem in the presence of stochastic volatility using asymptotic approximations when the volatility process is characterized by its time scales of fluctuation. This approach is tractable because it treats the incomplete markets problem as a perturbation around the complete market constant volatility problem for the value function, which is well-understood. When volatility is fast mean-reverting, this is a singular perturbation problem for a nonlinear Hamilton-Jacobi-Bellman PDE, while when volatility is slowly varying, it is a regular perturbation. These analyses can be combined for multifactor multiscale stochastic volatility models. The asymptotics shares remarkable similarities with the linear option pricing problem, which follows from some new properties of the Merton risk-tolerance function. We give examples in the family of mixture of power utilities and also we use our asymptotic analysis to suggest a "practical" strategy which does not require tracking the fast-moving volatility. In this paper, we present formal derivations of asymptotic approximations, and we provide a convergence proof in the case of power utility and single factor stochastic volatility. We assess our approximation in a particular case where there is an explicit solution.

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 Portfolio Optimization and Statistics in Stochastic Volatility Markets written by Carl Lindberg and published by . This book was released on 2005 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Portfolio Optimization Under Local Stochastic Volatility written by Matthew Lorig and published by . This book was released on 2015 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the finite horizon Merton portfolio optimization problem in a general local-stochastic volatility setting. Using model coefficient expansion techniques, we derive approximations for the both the value function and the optimal investment strategy. We also analyze the 'implied Sharpe ratio' and derive a series approximation for this quantity. The zeroth-order approximation of the value function and optimal investment strategy correspond to those obtained by Merton (1969) when the risky asset follows a geometric Brownian motion. The first-order correction of the value function can, for general utility functions, be expressed as a differential operator acting on the zeroth-order term. For power utility functions, higher order terms can also be computed as a differential operator acting on the zeroth-order term. We give a rigorous accuracy bound for the higher order approximations in this case in pure stochastic volatility models. A number of examples are provided in order to demonstrate numerically the accuracy of our approximations.

Download or read book Portfolio Optimization Under Multiscale Stochastic Volatility written by Keqin Gong and published by . This book was released on 2013 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, the classical Merton problem, a portfolio selection problem, is extended using multiscale volatility model which assumes that volatility of stock price depends on a fast scale process and a slow scale process. The Dynamic Programming Principle is used to establish the Hamilton-Jacobi-Bellman equation. An asymptotic method based on two small parameters from two scale factors, is applied in solving the equation to obtain an approximation of optimal trading strategy and value function, which is the expectation of utility of wealth in future. We also prove that when these two parameters are small, the error of our approximation of value function is small. Furthermore, we consider the counterparty risk in the portfolio selection problem, which means stock price has a jump at the default time and the stock is still tradable after default happens. In this scenario, an approximation of value function and optimal trading strategy is also derived and error of the approximation is estimated. Finally we use finite difference method to solve the problem and show how multiscale volatility model and counterparty default affect the results.

Download or read book Portfolio Optimization with Ambiguous Correlation and Stochastic Volatilities written by Jean-Pierre Fouque and published by . This book was released on 2019 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a continuous-time economy, we investigate the asset allocation problem among a risk-free asset and two risky assets with an ambiguous correlation between the two risky assets. The portfolio selection that is robust to the uncertain correlation is formulated as the utility maximization problem over the worst-case scenario with respect to the possible choice of correlation. Thus, it becomes a maximin problem. We solve the problem under the Black-Scholes model for risky assets with an ambiguous correlation using the theory of G-Brownian motions. We then extend the problem to stochastic volatility models for risky assets with an ambiguous correlation between risky asset returns. An asymptotic closed-form solution is derived for a general class of utility functions, including CRRA and CARA utilities, when stochastic volatilities are fast mean-reverting. We propose a practical trading strategy that combines information from the option implied volatility surfaces of risky assets through the ambiguous correlation.

Download or read book Optimal Portfolio Selection with Consumption Under Stochastic Volatility written by 葛蕾 and published by . This book was released on 2017 with total page 79 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 Merton s Portfolio Optimization Problem in a Black Scholes Market with Non Gaussian Stochastic Volatility of Ornstrein Uhlenbeck Type written by Fred E. Benth and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 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 On The Stability of Continuous Time Portfolio Problems with Stochastic Opportunity Set written by Holger Kraft and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we present some counter-examples to show that an uncritical application of the usual methods of continuous-time portfolio optimization can be misleading in the case of a stochastic opportunity set. Cases covered are problems with stochastic interest rates, stochastic volatility, and/or stochastic market price of risk. To classify the problems occurring with stochastic market coefficients we further introduce two notions of stability of portfolio problems.

Download or read book Dynamic Consumption and Portfolio Choice with Stochastic Volatility in Incomplete Markets written by George Chacko and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper examines the optimal consumption and portfolio-choice problem of long-horizon investors who have access to a riskless asset with constant return and a risky asset (quot;stocksquot;) with constant expected return and time-varying precision-the reciprocal of volatility. Markets are incomplete, and investors have recursive preferences defined over intermediate consumption. The paper obtains a solution to this problem which is exact for investors with unit elasticity of intertemporal substitution of consumption and approximate otherwise. The optimal portfolio demand for stocks includes an intertemporal hedging component that is negative when investors have coefficients of relative risk aversion larger than one, and the instantaneous correlation between volatility and stock returns is negative, as typically estimated from stock return data. Our estimates of the joint process for stock returns and precision (or volatility) using U.S. data confirm this finding. But we also find that stock return volatility does not appear to be variable and persistent enough to generate large intertemporal hedging demands.

Download or read book Merton s Portfolio Optimization Problem in a Black Scholes Market with Non Gaussian Stochastic Volatility of Ornstein Uhlenbeck Type written by Fred E. Benth and published by . This book was released on 2001 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Execute Trading Policies on Optimal Portfolio When Stochastic Volatility and Inflation Effect Were Considered written by Ashri Rahadi and published by . This book was released on 2016 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tempting to formulate the long-term investment strategy for investors who dynamically adjust her portfolio over her lifetime, we are interested to optimize the end-of-period terminal wealth using Bellman Principles. We designed the portfolio to be replete with risky asset and risk-less asset/fixed-income asset in the continuous framework. The stochastic volatility model is depicted in risky asset dynamic known as Constant Elasticity of Variance (CEV), because the empirical bias of Leverage effect in stock price evolution founded by Black Scholes can be directly examined. Meanwhile the bond pricing analysis was no longer classified as risk-free asset because it was analyzed under the stochastic Inflation and Interest rate of affine structures named Vasicek. Because we want to reflect their mean-reverting behavior as they're hovering around their long-term mean. Later, state space was constructed and portion of risky asset was elected to be control variables for supremum over value function. The concept of investment decision is intertemporal, as today decision affected tomorrow's, which finding its optimal rate would be trade-off for investor. For this, we framed the decision criteria with investor's utility function from class Decreasing Absolute Risk Aversion (DARA), the class that generally most investor mostly consistent with [Friend & Blumme 1975]. The problem description above can be represented as stochastic optimal control problem and it was solved with dynamic programming argument with modified verification theorem to tackle the issue of Stochastic Differential Equation well-posedness violation. Through stages of change variables, we were able to find the closed form trading solution from corresponding Hamilton Jacobi Bellman (HJB) equation. Compare to standard Merton model, our trading strategies strength are determining interest rate, inflation rate and degree of leverage for improvement and hence have inline economic logic reasoning for our solutions.

Download or read book Portfolio Optimization with Different Information Flow written by Caroline Hillairet and published by Elsevier. This book was released on 2017-02-10 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Portfolio Optimization with Different Information Flow recalls the stochastic tools and results concerning the stochastic optimization theory and the enlargement filtration theory.The authors apply the theory of the enlargement of filtrations and solve the optimization problem. Two main types of enlargement of filtration are discussed: initial and progressive, using tools from various fields, such as from stochastic calculus and convex analysis, optimal stochastic control and backward stochastic differential equations. This theoretical and numerical analysis is applied in different market settings to provide a good basis for the understanding of portfolio optimization with different information flow. Presents recent progress of stochastic portfolio optimization with exotic filtrations Shows you how to apply the tools of the enlargement of filtrations to resolve the optimization problem Uses tools from various fields from enlargement of filtration theory, stochastic calculus, convex analysis, optimal stochastic control, and backward stochastic differential equations