## Performance Bounds and Suboptimal Policies for Multi-Period Investment |
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Abstract:We consider dynamic trading of a portfolio of assets over a finite time horizon, with arbitrary time-varying distribution of asset returns. The goal is to maximize the total expected revenue from the portfolio, while respecting constraints on the portfolio such as a required terminal portfolio and leverage and risk limits. The revenue takes into account the gross cash generated in trades, transaction costs, and costs associated with the positions, such as fees for holding short positions. Our model has the form of a stochastic control problem with linear dynamics and convex cost function and constraints. We show how to use linear matrix inequality techniques and semidefinite programming to produce a quadratic bound on the value function, which in turn gives a bound on the optimal performance. This performance bound can be used to judge the performance obtained by any suboptimal policy. As a by-product of the performance bound computation, we obtain an approximate dynamic programming policy that requires the solution of a convex optimization problem, often a quadratic program, to determine the trades to carry out in each step. While we have no theoretical guarantee that the performance of our suboptimal policy is always near the performance bound (which would imply that it is nearly optimal) we observe that in numerical examples the two values are typically close. Joint work with M. Mueller, B. O’Donoghue and Y. Wang Published recordings: On-demand video. http://control.ee.ethz.ch/~valice/Boyd_LecOptimAppl_Mar2012.pdf |
Type of Seminar:Optimization and Applications Seminar |

Speaker:Prof. Stephen Boyd Electrical Engineering, Information Systems Laboratory, Stanford University | |

Date/Time:Mar 26, 2012 16:15 | |

Location:HG D 7.2, Rämistr. 101 | |

Contact Person:John Lygeros | |

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Biographical Sketch:Stephen P. Boyd is the Samsung Professor of Engineering, and Professor of Electrical Engineering in the Information Systems Laboratory at Stanford University. He also has a courtesy appointment in the Department of Management Science and Engineering, and is member of the Institute for Computational and Mathematical Engineering. His current research focus is on convex optimization applications in control, signal processing, and circuit design. Stephen P. Boyd received an AB degree in Mathematics, summa cum laude, from Harvard University in 1980, and a PhD in EECS from U. C. Berkeley in 1985. In 1985 he joined the faculty of Stanford’s Electrical Engineering Department. He has held visiting professor positions at Katholieke University (Leuven), McGill University (Montreal), Ecole Polytechnique Federale (Lausanne), Qinghua University (Beijing), Universite Paul Sabatier (Toulouse), Royal Institute of Technology (Stockholm), Kyoto University, Harbin Institute of Technology, NYU, and MIT. He holds an honorary doctorate from the Royal Institute of Technology (KTH), Stockholm. Stephen P. Boyd is the author of many research articles and three books: Linear Controller Design: Limits of Performance (with Craig Barratt, 1991), Linear Matrix Inequalities in System and Control Theory (with L. El Ghaoui, E. Feron, and V. Balakrishnan, 1994), and Convex Optimization (with Lieven Vandenberghe, 2004). His group has produced several open source tools, including CVX (with Michael Grant), a widely used parser-solver for convex optimization. Stephen P. Boyd has received many awards and honors for his research in control systems engineering and optimization, including an ONR Young Investigator Award and a Presidential Young Investigator Award. In 1992 he received the AACC Donald P. Eckman Award, which is given annually for the greatest contribution to the field of control engineering by someone under the age of 35. In 1993 he was elected Distinguished Lecturer of the IEEE Control Systems Society, and in 1999, he was elected Fellow of the IEEE, with citation: “For contributions to the design and analysis of control systems using convex optimization based CAD tools.” He has been invited to deliver more than 50 plenary and keynote lectures at major conferences in both control and optimization. |