Portfolio Selection under Time Delays: A Piecewise Dynamic Programming Approach

39 Pages Posted: 15 Feb 2017 Last revised: 6 Mar 2024

See all articles by Kai Li

Kai Li

Macquarie Business School, Macquarie University

Jun Liu

University of California, San Diego (UCSD) - Rady School of Management

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

Suggested Citation

Li, Kai and Liu, Jun, Portfolio Selection under Time Delays: A Piecewise Dynamic Programming Approach (January 28, 2024). Available at SSRN: https://ssrn.com/abstract=2916481 or http://dx.doi.org/10.2139/ssrn.2916481

Kai Li (Contact Author)

Macquarie Business School, Macquarie University ( email )

Level 6 4 Eastern Road, Macquarie University
North Ryde NSW 2109
Sydney, NSW 99999
Australia
435473800 (Phone)

Jun Liu

University of California, San Diego (UCSD) - Rady School of Management ( email )

9500 Gilman Drive
Rady School of Management
La Jolla, CA 92093
United States
858.534.2022 (Phone)
5858.534.0745 (Fax)

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