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 constant relative risk aversion and constant absolute risk aversion 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

  1. ambiguous correlation
  2. $G$-Brownian motion
  3. Hamilton--Jacobi--Bellman--Isaacs equation
  4. stochastic volatility

MSC codes

  1. 91G10
  2. 49L

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Information & Authors

Information

Published In

cover image SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Pages: 2309 - 2338
ISSN (online): 1095-7138

History

Submitted: 27 July 2015
Accepted: 6 July 2016
Published online: 7 September 2016

Keywords

  1. ambiguous correlation
  2. $G$-Brownian motion
  3. Hamilton--Jacobi--Bellman--Isaacs equation
  4. stochastic volatility

MSC codes

  1. 91G10
  2. 49L

Authors

Affiliations

Funding Information

National Research Foundation of South Africa
Claude Leon Foundation of South Africa
National Natural Science Foundation of China http://dx.doi.org/10.13039/501100001809

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