News-generated dependence and optimal portfolios for n stocks in a market of Barndorff-Nielsen and shephard type

Journal article, 2006

We consider Merton's portfolio optimization problem in a Black and Scholes market with non-Gaussian stochastic volatility of Ornstein-Uhlenbeck type. The investor can trade in n stocks and a risk-free bond. We assume that the dependence between stocks lies in that they partly share the Ornstein-Uhlenbeck processes of the volatility. We refer to these as news processes, and interpret this as that dependence between stocks lies solely in their reactions to the same news. The model is primarily intended for assets that are dependent, but not too dependent, such as stocks from different branches of industry. We show that this dependence generates covariance, and give statistical methods for both the fitting and verification of the model to data. Using dynamic programming, we derive and verify explicit trading strategies and Feynman-Kac representations of the value function for power utility.