2012, ISBN: 9781249098942

<br /> There is a recent interest in modeling the one period stock returns (i.e. the relative price changes) by elliptical models instead of Gaussian ones. Most… Mehr…

<br /> There is a recent interest in modeling the one period stock returns (i.e. the relative price changes) by elliptical models instead of Gaussian ones. Most previous work on non-Gaussian distributions focuses on the tails and uses in particular the Student t distribution because of its power law tails. We build a new model that fits the empirical data reasonably well both in the tails and the central region. The new model is a sub-family of the elliptical models. Its joint distribution of multi-asset returns has the feature that the probability density blows up at the origin. The exponential tail of this model is also a plausible fit to the data in the tails. <br /> <br /> Assuming the elliptical models, we study the uncertainty of a mean variance portfolio optimization problem replacing population quantities by standard estimators. We find the asymptotic expansion and tail behavior of the optimal solutions for large dimensional portfolio where p, the number of variables in the problem, is of the same order of magnitude as n, the number of observations used to estimate the parameters. Our approach is similar to El Karoui's work, but our mean variance portfolio optimization setting is different from his. <br /> <br /> Decision theory suggests us the optimal portfolio choice with mean variance utility is the solution of the Bayesian mean-variance portfolio optimization problem. The Bayesian approach allows the investor to reflect financial information or private views about the future return-generating process rather than just the historical returns. It is more robust than the mean variance portfolio optimization problem replacing population quantities by the standard sample estimators, assuming non-Gaussianity of the asset returns. Moreover, the solution can be easily computed by certain Monte Carlo method which utilize auxiliary variables. Our new one period model can be extended to a new stochastic volatility model. The Bayesian asset allocation for the one period model also works for the new stochastic volatility model. <br /> Weight:0.64 lbs, ProQuest, UMI Dissertation Publishing, 7/17/2012 0:00:00<