Applications of Continuous-Time Stochastic Control in Portfolio Optimization

This dissertation applies stochastic control theory in portfolio optimization problems in two different scenarios.In the first part, we consider a partially-informed trader who does not observe the true drift of a financial asset. Under price dynamics with stochastic unobserved drift, including cases of mean-reversion and momentum dynamics, we take a filtering approach to solve explicitly for trading strategies maximizing expected logarithmic, exponential, and power utility. In the second part, we study the problem of dynamically trading multiple futures contracts subject to portfolio constraints under a stochastic basis model. The spreads between futures and spot prices are modeled by a multidimensional scaled Brownian bridge to account for their convergence at maturity. The optimal trading strategies are determined from a utility maximization problem with risk preferences of CRRA type.