Stochastic Control Methods for Dynamic Futures Portfolios

Abstract

In this thesis, we discuss systematic methods to futures trading and analyze the mathematical problems that arise from trading futures. Firstly, we analyze the dynamic futures trading strategies under a general multifactor Gaussian framework. Our framework captures a number of well-known models, like the Schwartz model and Central Tendency Ornstein-Uhlenbeck (CTOU) model. We also present a new multiscale CTOU model within this framework. Secondly, we study the problem of dynamically trading futures in a general regime switching market in which the stochastic market regime is represented by a continuous-time finite-state Markov chain. As examples within our stochastic framework, we consider the Regime-Switching Geometric Brownian Motion (RS-GBM) model and Regime-Switching Exponential Ornstein-Uhlenbeck (RS-XOU) model. Thirdly, we model the stochastic spreads between the underlying spot price and associated futures prices by a multidimensional scaled Brownian bridge. In addition, the portfolio optimization problem is incorporated with constraints on the futures position. Our general setup captures the dollar neutral and market neutral constraints, which are widely used in industry. For all three problems, we apply utility maximization approaches to determine the optimal futures trading strategy. This leads to the analysis of the corresponding Hamilton-Jacobi-Bellman (HJB) equations, whose solutions are obtained explicitly or in semi-explicit form. Numerical examples are provided to illustrate the investor's certainty equivalent, optimal futures positions, and wealth process for each problem.