| The theme of this dissertation is dynamic hedging strategies. In simple terms, hedging means guarding against risk. In the context of financial investment, hedging refers to risk reduction by transferring the risk of return to others, as opposed to the approach of portfolio diversification. A dynamic hedging strategy is an investment strategy involving the ongoing reallocation of financial assets over time, with the goal of attaining the desired return on investment with minimum risk by hedging.;Many financial instruments are called derivative instruments, or contingent claims for they so exist and are priced only because of the existence and the prevailing price levels of some underlying securities. They fall into two main categories, namely, futures contracts and options. Both of these can be effectively used as hedging tools. In this dissertation, we focus on using financial futures contracts as a hedging tool and consider the problem of searching for an optimal dynamic hedging strategy from a systems science perspective. By defining the wealth of an investor as a time-varying system state variable to be controlled, a dynamic hedging strategy is viewed as a feedback control policy for a dynamical system driven by stochastic price-movements in the market. A class of nonlinear conditional heteroskedastic models, namely, autoregressive conditional heteroskedastic (ARCH) models, is used to describe the stochastic nature of price movements. Control performance is measured with a quadratic performance index defined as the mean squared-deviations of the actual growth-path of wealth from a specified target track. The optimal dynamic hedging strategy for the simplest case of a single-security bivariate ARCH model of order one has been fully developed. The result is a non-myopic Markovian strategy.;In formulating the above multi-period nonlinear sequential optimization problem, we consider only discrete-time hedging scenarios with finite horizons. Additionally, we also have extended the single-security dynamic hedging formulation to a multiple-security multiple-investor dynamic portfolio hedging scenario, which should be of great interest to many portfolio management and investment consultants alike. Finally, real-world data related to the U.S. Treasure bill market and the corresponding 90-day Treasury bills futures market are chosen for the purpose of empirical study. |
