Portfolio Selection under Time Delays: A Piecewise Dynamic Programming Approach
39 Pages Posted: 15 Feb 2017 Last revised: 6 Mar 2024
Date Written: January 28, 2024
Abstract
Many economic dynamics depend explicitly on delayed variables. Examples include price momentum and time to build. This paper develops a method to solve optimal decision problems for this class of economic dynamics. The optimal policy depends on historical paths, which are characterized by new state variables. The new variables are different for different horizons, and the number of them increases without bound. In a portfolio choice application with an incomplete market, we analytically derive the optimal portfolio weights.
Keywords: Dynamic choice, path dependence, sufficient statistic, stochastic delay differential equations, piecewise dynamic programming
JEL Classification: C61, G11, G12
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