A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability
Michael W. Brandt
Duke University - Fuqua School of Business; National Bureau of Economic Research (NBER)
University of Lausanne; Swiss Finance Institute
Nova School of Business and Economics; National Bureau of Economic Research (NBER); Centre for Economic Policy Research (CEPR)
Jonathan R. Stroud
University of Pennsylvania - Statistics Department
Review of Financial Studies, Vol. 18, No. 3, pp. 831-873, 2005
We present a simulation-based method for solving discrete-time portfolio choice problems involving non-standard preferences, a large number of assets with arbitrary return distribution, and, most importantly, a large number of state variables with potentially path-dependent or non-stationary dynamics. The method is flexible enough to accommodate intermediate consumption, portfolio constraints, parameter and model uncertainty, and learning. We first establish the properties of the method for the portfolio choice between a stock index and cash when the stock returns are either iid or predictable by the dividend yield. We then explore the problem of an investor who takes into account the predictability of returns but is uncertain about the parameters of the data generating process. The investor chooses the portfolio anticipating that future data realizations will contain useful information to learn about the true parameter values.
Keywords: time optimal control problems, Neumann parabolic equations with an infinite number of variables, Dubovitskii-Milyutin theorem, conical approximations, optimality conditions, Weierstrass theoremAccepted Paper Series
Date posted: February 29, 2008
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