Portfolio Optimization with Ambiguous Correlation and Stochastic Volatilities

SIAM J. Control Optim., 54(5), 2309-2338, 2016

30 Pages Posted: 14 Aug 2014 Last revised: 17 Mar 2017

See all articles by Jean-Pierre Fouque

Jean-Pierre Fouque

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

Chi Seng Pun

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences

Hoi Ying Wong

The Chinese University of Hong Kong (CUHK) - Department of Statistics

Date Written: August 13, 2014

Abstract

In a continuous-time economy, we investigate the asset allocation problem among a risk-free asset and two risky assets with an ambiguous correlation between the two risky assets. The portfolio selection that is robust to the uncertain correlation is formulated as the utility maximization problem over the worst-case scenario with respect to the possible choice of correlation. Thus, it becomes a maximin problem. We solve the problem under the Black-Scholes model for risky assets with an ambiguous correlation using the theory of G-Brownian motions. We then extend the problem to stochastic volatility models for risky assets with an ambiguous correlation between risky asset returns. An asymptotic closed-form solution is derived for a general class of utility functions, including CRRA and CARA utilities, when stochastic volatilities are fast mean-reverting. We propose a practical trading strategy that combines information from the option implied volatility surfaces of risky assets through the ambiguous correlation.

Keywords: Ambiguous correlation, G-Brownian motion, Hamilton-Jacobi-Bellman-Isaacs equation, Stochastic volatility

Suggested Citation

Fouque, Jean-Pierre and Pun, Chi Seng and Wong, Hoi Ying, Portfolio Optimization with Ambiguous Correlation and Stochastic Volatilities (August 13, 2014). SIAM J. Control Optim., 54(5), 2309-2338, 2016. Available at SSRN: https://ssrn.com/abstract=2479796 or http://dx.doi.org/10.2139/ssrn.2479796

Jean-Pierre Fouque

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

United States

Chi Seng Pun (Contact Author)

Nanyang Technological University (NTU) - School of Physical and Mathematical Sciences ( email )

SPMS-MAS-05-22
21 Nanyang Link
Singapore, 637371
Singapore
(+65) 6513 7468 (Phone)

HOME PAGE: http://www.ntu.edu.sg/home/cspun/

Hoi Ying Wong

The Chinese University of Hong Kong (CUHK) - Department of Statistics ( email )

Shatin, N.T.
Hong Kong

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