Abstracts
Tuesday June 3, 16:30-17:00 | session 3.2 | Portfolio Optimization | room CD
In this paper we develop a new proof of Strassen's theorem, which stands a necessary and sufficient condition for the existence of a martingale measure with given marginals. The initial proof, due to Strassen is based on an application of Hahn-Banach's Theorem. Our proof is based on utility maximization technics introduced by Rogers for the fundamental theorem of asset pricing. We adapt his general idea to suit to the martingale optimal transport, and we derive a financial proof of this result. We finally discuss the case of Kellerer's theorem, which is the continuous time version of Strassen's theorem.
Tuesday June 3, 17:00-17:30 | session 3.2 | Portfolio Optimization | room CD
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.