Perturbation Analysis for Investment Portfolios Under Partial Information with Expert Opinions

SIAM J. Control Optim., 55(3), (2017) pp. 1534–1566.

NYU Tandon Research Paper No. 2532051

32 Pages Posted: 30 Nov 2014 Last revised: 26 Jun 2017

See all articles by Andrew Papanicolaou

Andrew Papanicolaou

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

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering

Jean-Pierre Fouque

University of California, Santa Barbara (UCSB) - Statistics & Applied Probablity

Date Written: November 29, 2014

Abstract

We analyze the Merton portfolio optimization problem when the growth rate is an unobserved Gaussian process whose level is estimated by filtering from observations of the stock price. We use the Kalman filter to track the hidden state(s) of expected returns given the history of asset prices, and then use this filter as input to a portfolio problem with an objective to maximize expected terminal utility. Our results apply for general concave utility functions.We incorporate time-scale separation in the fluctuations of the returns process, and utilize singular and regular perturbation analysis on the associated partial information HJB equation, which leads to an intuitive interpretation of the additional risk caused by uncertainty in expected returns.The results are an extension of the partially-informed investment strategies obtained by the Black-Litterman model, wherein investors' views on upcoming performance are incorporated into the optimization along with any degree of uncertainty that the investor may have in these views.

Keywords: Filtering, Control, Hamilton-Jacobi-Bellman equation, Portfolio optimization, partial information, expert opinions.

JEL Classification: G12, G13, G17

Suggested Citation

Papanicolaou, Andrew and Sircar, Ronnie and Fouque, Jean-Pierre, Perturbation Analysis for Investment Portfolios Under Partial Information with Expert Opinions (November 29, 2014). SIAM J. Control Optim., 55(3), (2017) pp. 1534–1566.; NYU Tandon Research Paper No. 2532051. Available at SSRN: https://ssrn.com/abstract=2532051 or http://dx.doi.org/10.2139/ssrn.2532051

Andrew Papanicolaou (Contact Author)

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

6 Metrotech Center
Brooklyn, NY 11201
United States

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering ( email )

Princeton, NJ 08544
United States

Jean-Pierre Fouque

University of California, Santa Barbara (UCSB) - Statistics & Applied Probablity ( email )

United States

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