Journal
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Volume 54, Issue 5, Pages 2309-2338Publisher
SIAM PUBLICATIONS
DOI: 10.1137/15M1032533
Keywords
ambiguous correlation; G-Brownian motion; Hamilton-Jacob-Bellman-Isaacs equation; stochastic volatility
Categories
Funding
- Direct Research Grant of Chinese University of Hong Kong
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1409434] Funding Source: National Science Foundation
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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.
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