Dimension Reduction in Discrete Time Portfolio Optimization with Partial Information

December 2013, SIAM J. Finan. Math., 4(1), 916–960

37 Pages Posted: 25 Oct 2012 Last revised: 26 Jun 2017

See all articles by Andrew Papanicolaou

Andrew Papanicolaou

NYU Tandon School of Engineering, Department of Finance and Risk Engineering

Date Written: December 10, 2013

Abstract

This paper considers the problem of portfolio optimization in a market with partial information and discretely observed price processes. Partial information refers to the setting where assets have unobserved factors in the rate of return and the level of volatility. Standard filtering techniques are used to compute the posterior distribution of the hidden variables, but there is difficulty in finding the optimal portfolio because the dynamic programming problem is non-Markovian. However, fast time scale asymptotics can be exploited to obtain an approximate dynamic program (ADP) that is Markovian and is therefore much easier to compute. Of consideration is a model where the latent variables (also referred to as hidden states) have fast mean reversion to an invariant distribution that is parameterized by a Markov chain θt, where θt represents the regime-state of the market and reverts to its own invariant distribution over a much longer time scale. Data and numerical examples are also presented, and there appears to be evidence that unobserved drift results in an information premium.

Keywords: filtering, portfolio optimization, partial information

JEL Classification: G12, G13, G17

Suggested Citation

Papanicolaou, Andrew, Dimension Reduction in Discrete Time Portfolio Optimization with Partial Information (December 10, 2013). December 2013, SIAM J. Finan. Math., 4(1), 916–960. Available at SSRN: https://ssrn.com/abstract=2164817 or http://dx.doi.org/10.2139/ssrn.2164817

Andrew Papanicolaou (Contact Author)

NYU Tandon School of Engineering, Department of Finance and Risk Engineering ( email )

6 Metrotech Center
Brooklyn, NY 11201
United States

Register to save articles to
your library

Register

Paper statistics

Downloads
153
Abstract Views
1,061
rank
198,541
PlumX Metrics