Abstracts

In a continuous-time economy, we investigate the asset location problem among a risk-free asset and two risky assets with an ambiguous correlation between the two risky assets. The portfolio selection robust to the uncertain correlation is formulated as the utility maximization problem over the worst-case scenario with respect 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 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. 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 offer a practical trading strategy which combines information from option implied volatility surfaces of risky assets through the ambiguous correlation.