Penalty Methods For Continuous Time Portfolio Selection With Proportional Transaction Costs
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Author | : Min Dai |
Publisher | : |
Total Pages | : 25 |
Release | : 2008 |
Genre | : |
ISBN | : |
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.
Author | : Tusheng Zhang |
Publisher | : World Scientific |
Total Pages | : 465 |
Release | : 2012 |
Genre | : Business & Economics |
ISBN | : 9814383589 |
This volume is a collection of solicited and refereed articles from distinguished researchers across the field of stochastic analysis and its application to finance. The articles represent new directions and newest developments in this exciting and fast growing area. The covered topics range from Markov processes, backward stochastic differential equations, stochastic partial differential equations, stochastic control, potential theory, functional inequalities, optimal stopping, portfolio selection, to risk measure and risk theory. It will be a very useful book for young researchers who want to learn about the research directions in the area, as well as experienced researchers who want to know about the latest developments in the area of stochastic analysis and mathematical finance. Sample Chapter(s). Editorial Foreword (58 KB). Chapter 1: Non-Linear Evolution Equations Driven by Rough Paths (399 KB). Contents: Non-Linear Evolution Equations Driven by Rough Paths (Thomas Cass, Zhongmin Qian and Jan Tudor); Optimal Stopping Times with Different Information Levels and with Time Uncertainty (Arijit Chakrabarty and Xin Guo); Finite Horizon Optimal Investment and Consumption with CARA Utility and Proportional Transaction Costs (Yingshan Chen, Min Dai and Kun Zhao); MUniform Integrability of Exponential Martingales and Spectral Bounds of Non-Local Feynman-Kac Semigroups (Zhen-Qing Chen); Continuous-Time Mean-Variance Portfolio Selection with Finite Transactions (Xiangyu Cui, Jianjun Gao and Duan Li); Quantifying Model Uncertainties in the Space of Probability Measures (J Duan, T Gao and G He); A PDE Approach to Multivariate Risk Theory (Robert J Elliott, Tak Kuen Siu and Hailiang Yang); Stochastic Analysis on Loop Groups (Shizan Fang); Existence and Stability of Measure Solutions for BSDE with Generators of Quadratic Growth (Alexander Fromm, Peter Imkeller and Jianing Zhang); Convex Capital Requirements for Large Portfolios (Hans FAllmer and Thomas Knispel); The Mixed Equilibrium of Insider Trading in the Market with Rational Expected Price (Fuzhou Gong and Hong Liu); Some Results on Backward Stochastic Differential Equations Driven by Fractional Brownian Motions (Yaozhong Hu, Daniel Ocone and Jian Song); Potential Theory of Subordinate Brownian Motions Revisited (Panki Kim, Renming Song and Zoran Vondraiek); Research on Social Causes of the Financial Crisis (Steven Kou); Wick Formulas and Inequalities for the Quaternion Gaussian and -Permanental Variables (Wenbo V Li and Ang Wei); Further Study on Web Markov Skeleton Processes (Yuting Liu, Zhi-Ming Ma and Chuan Zhou); MLE of Parameters in the Drifted Brownian Motion and Its Error (Lemee Nakamura and Weian Zheng); Optimal Partial Information Control of SPDEs with Delay and Time-Advanced Backward SPDEs (Bernt yksendal, Agn s Sulem and Tusheng Zhang); Simulation of Diversified Portfolios in Continuous Financial Markets (Eckhard Platen and Renata Rendek); Coupling and Applications (Feng-Yu Wang); SDEs and a Generalised Burgers Equation (Jiang-Lun Wu and Wei Yang); Mean-Variance Hedging in the Discontinuous Case (Jianming Xia). Readership: Graduates and researchers in stochatic analysis and mathematical finance.
Author | : Xin Guo |
Publisher | : CRC Press |
Total Pages | : 414 |
Release | : 2017-01-06 |
Genre | : Business & Economics |
ISBN | : 1315354357 |
The first part of this book discusses institutions and mechanisms of algorithmic trading, market microstructure, high-frequency data and stylized facts, time and event aggregation, order book dynamics, trading strategies and algorithms, transaction costs, market impact and execution strategies, risk analysis, and management. The second part covers market impact models, network models, multi-asset trading, machine learning techniques, and nonlinear filtering. The third part discusses electronic market making, liquidity, systemic risk, recent developments and debates on the subject.
Author | : |
Publisher | : |
Total Pages | : 402 |
Release | : 2009 |
Genre | : Finance |
ISBN | : |
Author | : Baojun Bian |
Publisher | : |
Total Pages | : 46 |
Release | : 2019 |
Genre | : |
ISBN | : |
Many finance problems can be formulated as a singular stochastic control problem, where the associated Hamilton-Jacobi-Bellman (HJB) equation takes the form of variational inequality and its penalty approximation equation is linked to a regular control problem. The penalty method, as a finite difference scheme for the penalty equation, has been widely used to numerically solve singular control problems, and its convergence analysis in literature relies on the uniqueness of solution to the original HJB equation problem. We consider a singular stochastic control problem arising from continuous-time portfolio selection with capital gains tax, where the associated HJB equation problem admits infinitely many solutions. We show that the penalty method still works and converges to the value function which is the minimal (viscosity) solution of the HJB equation problem. Numerical results are presented to demonstrate the efficiency of the penalty method and to better understand optimal investment strategy in the presence of capital gains tax. Our approach sheds light on the robustness of the penalty method for general singular stochastic control problems.
Author | : Andriy Demchuk |
Publisher | : |
Total Pages | : 27 |
Release | : 1999 |
Genre | : |
ISBN | : |
Author | : |
Publisher | : ScholarlyEditions |
Total Pages | : 1104 |
Release | : 2013-05-01 |
Genre | : Political Science |
ISBN | : 1490109854 |
Issues in Industrial Relations and Management: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Management Science. The editors have built Issues in Industrial Relations and Management: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Management Science in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Industrial Relations and Management: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Author | : Constantin Alexandru Filitti |
Publisher | : |
Total Pages | : 134 |
Release | : 2004 |
Genre | : Portfolio-Management / Dynamische Optimierung / Betriebswirtschaftliche Investitionstheorie / Stochastischer Prozess |
ISBN | : |
Author | : Jan Palczewski |
Publisher | : |
Total Pages | : 38 |
Release | : 2014 |
Genre | : |
ISBN | : |
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.
Author | : Nikolay Andreev |
Publisher | : |
Total Pages | : 54 |
Release | : 2016 |
Genre | : |
ISBN | : |
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.