An Affine Control Method for Optimal Dynamic Asset Allocation with Transaction Costs

In this paper, we present a novel and computationally efficient approach to constrained discrete-time dynamic asset allocation over multiple periods. This technique is able to control portfolio expectation and variance at both final and intermediate stages of the decision horizon and may account for proportional transaction costs and intertemporal dependence of the return process. A key feature of the proposed method is the use of a linearly parameterized class of feedback control policies, which permits us to obtain explicit analytic expressions for the portfolio statistics over time. These expressions are proved to be convex in the decision parameters, and hence, under these control laws, the multistage problem is formulated and solved by means of efficient tools for quadratic or second-order-cone convex programming.

[1]  R. Wets,et al.  Stochastic programming , 1989 .

[2]  J. Löfberg.  Minimax approaches to robust model predictive control , 2003 .

[3]  Michael W. Brandt.  Estimating Portfolio and Consumption Choice: A Conditional Euler Equations Approach , 1999 .

[4]  Antonio Alonso Ayuso,et al.  Introduction to Stochastic Programming , 2009 .

[5]  O. Costa,et al.  Multiperiod Mean-Variance Optimization with Intertemporal Restrictions , 2007 .

[6]  Peter Kall,et al.  Stochastic Programming , 1995 .

[7]  E. Fama.  EFFICIENT CAPITAL MARKETS: A REVIEW OF THEORY AND EMPIRICAL WORK* , 1970 .

[8]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[9]  Georg Ch. Pflug,et al.  Scenario tree generation for multiperiod financial optimization by optimal discretization , 2001, Math. Program..

[10]  Alexander Shapiro,et al.  Lectures on Stochastic Programming: Modeling and Theory , 2009 .

[11]  B. Ross Barmish,et al.  On Trading of Equities: A Robust Control Paradigm , 2008 .

[12]  W. Ziemba,et al.  Worldwide asset and liability modeling , 1998 .

[13]  R. C. Merton,et al.  AN INTERTEMPORAL CAPITAL ASSET PRICING MODEL , 1973 .

[14]  T. Roncalli,et al.  Strategic Asset Allocation , 2011 .

[15]  Yuri Ermoliev,et al.  Numerical techniques for stochastic optimization , 1988 .

[16]  Alexander Shapiro,et al.  On complexity of multistage stochastic programs , 2006, Oper. Res. Lett..

[17]  John R. Birge.  Multistage Stochastic Planning Models Using Piecewise Linear Response Functions , 1989 .

[18]  R. C. Merton,et al.  Optimum Consumption and Portfolio Rules in a Continuous-Time Model* , 1975 .

[19]  Maria Grazia Speranza,et al.  Conditional value at risk and related linear programming models for portfolio optimization , 2007, Ann. Oper. Res..

[20]  Marc C. Steinbach,et al.  Markowitz Revisited: Mean-Variance Models in Financial Portfolio Analysis , 2001, SIAM Rev..

[21]  Nalan Gülpinar,et al.  Worst-case robust decisions for multi-period mean-variance portfolio optimization , 2007, Eur. J. Oper. Res..

[22]  J. Lofberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508).

[23]  J.A. Primbs,et al.  Portfolio Optimization Applications of Stochastic Receding Horizon Control , 2007, 2007 American Control Conference.

[24]  Norio Hibiki.  Multi-period stochastic optimization models for dynamic asset allocation , 2006 .

[25]  Burton G. Malkiel,et al.  Efficient Market Hypothesis , 1991 .

[26]  Giuseppe Carlo Calafiore,et al.  Multi-period portfolio optimization with linear control policies , 2008, Autom..

[27]  H.P. Geering,et al.  Model predictive control for portfolio selection , 2006, 2006 American Control Conference.

[28]  Florian Herzog,et al.  Stochastic Model Predictive Control And Portfolio Optimization , 2007 .

[29]  John R. Birge,et al.  Stochastic Programming Computation and Applications , 1997, INFORMS J. Comput..

[30]  Mustafa Ç. Pinar,et al.  Robust scenario optimization based on downside-risk measure for multi-period portfolio selection , 2007, OR Spectr..

[31]  George B. Dantzig,et al.  Multi-stage stochastic linear programs for portfolio optimization , 1993, Ann. Oper. Res..

[32]  Berç Rustem,et al.  Multistage Stochastic Programming in Computational Finance , 2002 .

[33]  A. Ben-Tal,et al.  Adjustable robust solutions of uncertain linear programs , 2004, Math. Program..

[34]  R. C. Merton,et al.  Optimum consumption and portfolio rules in a continuous - time model Journal of Economic Theory 3 , 1971 .