Multiagent Cooperative Search for Portfolio Selection

We present a new multiagent model for the multiperiod portfolio selection problem. A system of cooperative agents divide initial wealth and follow individual worst-case optimal investment strategies from random portfolios, sharing their final profits and losses. The multiagent system achieves better average-case performance than a single agent with the same initial wealth in a simple stochastic market. A further increase in performance is achieved through communication of hints between agents and probabilistic strategy-switching. However, this explicit cooperation is redundant in a market that approximates the Capital Asset Pricing Model, a model of equilibrium stock price dynamics. Journal of Economic Literature Classification Numbers: C63, C73, D83, G11.

[1]  B A Huberman,et al.  Cooperative Solution of Constraint Satisfaction Problems , 1991, Science.

[2]  H. Young,et al.  The Evolution of Conventions , 1993 .

[3]  Wolfgang Ertel,et al.  Optimal parallelization of Las Vegas algorithms , 1993, Forschungsberichte, TU Munich.

[4]  Paul R. Milgrom,et al.  Adaptive and sophisticated learning in normal form games , 1991 .

[5]  Mark S. Boddy,et al.  Solving Time-Dependent Planning Problems , 1989, IJCAI.

[6]  Robert Buff.  Continuous Time Finance , 2002 .

[7]  Umesh V. Vazirani,et al.  "Go with the winners" algorithms , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[8]  D. A. Sprott,et al.  Foundations of Statistical Inference. , 1972 .

[9]  Tad Hogg,et al.  Solving the Really Hard Problems with Cooperative Search , 1993, AAAI.

[10]  F. Black,et al.  The Capital Asset Pricing Model: Some Empirical Tests , 2006 .

[11]  E. Kalai,et al.  Rational Learning Leads to Nash Equilibrium , 1993 .

[12]  Erik Ordentlich,et al.  Universal portfolios with side information , 1996, IEEE Trans. Inf. Theory.

[13]  E. Prescott,et al.  Investment Under Uncertainty , 1971 .

[14]  R. Rob,et al.  Learning, Mutation, and Long Run Equilibria in Games , 1993 .

[15]  Andrew B. Kahng,et al.  A new adaptive multi-start technique for combinatorial global optimizations , 1994, Oper. Res. Lett..

[16]  W. Sharpe.  Portfolio Theory and Capital Markets , 1970 .

[17]  T. Cover.  Universal Portfolios , 1996 .

[18]  S. Kauffman,et al.  Towards a general theory of adaptive walks on rugged landscapes. , 1987, Journal of theoretical biology.

[19]  F. Post,et al.  An Economics Approach to Hard Computational Problems , 1997 .

[20]  W. Arthur.  Inductive Reasoning and Bounded Rationality , 1994 .

[21]  R. Palmer,et al.  Asset Pricing Under Endogenous Expectations in an Artificial Stock Market , 1996 .

[22]  H. Simon,et al.  From substantive to procedural rationality , 1976 .

[23]  R. C. Merton,et al.  Continuous-Time Finance , 1990 .

[24]  P. Samuelson.  Lifetime Portfolio Selection by Dynamic Stochastic Programming , 1969 .

[25]  Adam Tauman Kalai,et al.  Universal Portfolios With and Without Transaction Costs , 2004, Machine Learning.

[26]  A. Lo,et al.  THE ECONOMETRICS OF FINANCIAL MARKETS , 1996, Macroeconomic Dynamics.

[27]  Vipin Kumar,et al.  On the Efficiency of Parallel Backtracking , 1993, IEEE Trans. Parallel Distributed Syst..

[28]  Eduardo S. Schwartz,et al.  Investment Under Uncertainty. , 1994 .

[29]  A. Rubinstein.  Modeling Bounded Rationality , 1998 .

[30]  Joshua M. Epstein,et al.  Growing Artificial Societies: Social Science from the Bottom Up , 1996 .

[31]  Vipin Kumarxz,et al.  On the Eeciency of Parallel Backtracking , 1992 .

[32]  Edmund H. Durfee,et al.  Learning nested agent models in an information economy , 1998, J. Exp. Theor. Artif. Intell..

[33]  David Zuckerman,et al.  Optimal speedup of Las Vegas algorithms , 1993, [1993] The 2nd Israel Symposium on Theory and Computing Systems.

[34]  Sandy Irani,et al.  Online computation , 1996 .

[35]  S HochbaDorit.  Approximation Algorithms for NP-Hard Problems , 1997 .

[36]  Catherine A. Schevon,et al.  Optimization by simulated annealing: An experimental evaluation , 1984 .

[37]  Manfred K. Warmuth,et al.  The Weighted Majority Algorithm , 1994, Inf. Comput..

[38]  Thomas M. Cover,et al.  Empirical Bayes stock market portfolios , 1986 .

[39]  M. Rothschild.  A two-armed bandit theory of market pricing , 1974 .

[40]  Dorit S. Hochbaum,et al.  Approximation Algorithms for NP-Hard Problems , 1996 .

[41]  Michael C. Jensen,et al.  Studies in the Theory of Capital Markets. , 1973 .

[42]  Víctor Dalmau,et al.  A Dichotomy Theorem for Learning Quantified Boolean Formulas , 1997, COLT.

[43]  Dimitri P. Bertsekas,et al.  Dynamic Programming: Deterministic and Stochastic Models , 1987 .

[44]  Hector J. Levesque,et al.  A New Method for Solving Hard Satisfiability Problems , 1992, AAAI.

[45]  Yoram Singer,et al.  A Comparison of New and Old Algorithms for a Mixture Estimation Problem , 2004, Machine Learning.

[46]  Moshe Tennenholtz,et al.  Adaptive Load Balancing: A Study in Multi-Agent Learning , 1994, J. Artif. Intell. Res..

[47]  Neil D. Pearson,et al.  Consumption and Portfolio Policies With Incomplete Markets and Short‐Sale Constraints: the Finite‐Dimensional Case , 1991 .

[48]  Anna Nagurney,et al.  Foundations of Financial Economics , 1997 .

[49]  Jonathan Gratch,et al.  Adaptive Problem-solving for Large-scale Scheduling Problems: A Case Study , 1996, J. Artif. Intell. Res..

[50]  Edmund H. Durfee,et al.  A Rigorous, Operational Formalization of Recursive Modeling , 1995, ICMAS.

[51]  P. Samuelson.  LIFETIME PORTFOLIO SELECTION BY DYNAMIC STOCHASTIC PROGRAMMING , 1969 .

[52]  Erik Ordentlich,et al.  On-line portfolio selection , 1996, COLT '96.

[53]  Glenn Ellison,et al.  Rules of Thumb for Social Learning , 1993, Journal of Political Economy.

[54]  Yoram Singer,et al.  A Comparison of New and Old Algorithms for a Mixture Estimation Problem , 1995, COLT '95.

[55]  Pierre-Louis Lions,et al.  On mathematical finance , 2000 .

[56]  K. Arrow,et al.  The Economics of Uncertainty. , 1970 .

[57]  William A. Kornfeld.  The Use of Parallelism to Implement a Heuristic Search , 1981, IJCAI.

[58]  Robert H. Crites,et al.  Multiagent reinforcement learning in the Iterated Prisoner's Dilemma. , 1996, Bio Systems.

[59]  Kevin Knight,et al.  Are Many Reactive Agents Better Than a Few Deliberative Ones? , 1993, IJCAI.

[60]  S. Bikhchandani,et al.  You have printed the following article : A Theory of Fads , Fashion , Custom , and Cultural Change as Informational Cascades , 2007 .

[61]  Manfred K. Warmuth,et al.  Additive versus exponentiated gradient updates for linear prediction , 1995, STOC '95.

[62]  Bernardo A. Huberman,et al.  The performance of cooperative processes , 1990 .

[63]  D. Fudenberg,et al.  Consistency and Cautious Fictitious Play , 1995 .

[64]  Haim Levy.  Risk and Return--An Experimental Analysis , 1997 .

[65]  David M. Kreps,et al.  Learning Mixed Equilibria , 1993 .

[66]  P. Algoet.  UNIVERSAL SCHEMES FOR PREDICTION, GAMBLING AND PORTFOLIO SELECTION' , 1992 .

[67]  Cecilia R. Aragon,et al.  Optimization by Simulated Annealing: An Experimental Evaluation; Part I, Graph Partitioning , 1989, Oper. Res..

[68]  Nicolò Cesa-Bianchi,et al.  Gambling in a rigged casino: The adversarial multi-armed bandit problem , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[69]  T. Cover,et al.  Asymptotic optimality and asymptotic equipartition properties of log-optimum investment , 1988 .

[70]  Stuart J. Russell,et al.  Principles of Metareasoning , 1989, Artif. Intell..

[71]  Yoram Singer,et al.  On‐Line Portfolio Selection Using Multiplicative Updates , 1998, ICML.

[72]  Alexander Rosenberg,et al.  Method and Appraisal in Economics. , 1976 .

[73]  Joshua M. Epstein,et al.  Growing Artificial Societies: Social Science from the Bottom Up , 1996 .

[74]  W. Arthur,et al.  The Economy as an Evolving Complex System II , 1988 .

[75]  T. Andersen.  THE ECONOMETRICS OF FINANCIAL MARKETS , 1998, Econometric Theory.