Optimal control of option portfolios and applications

We present an expected utility maximisation framework for optimally controlling a portfolio of options. By combining the replications approach to option pricing with ideas of the martingale approach to (stock) portfolio optimisation we arrive at an explicit solution of the option portfolio problem. Its characteristics are illustrated by some specific examples. As an application, we calculate an optimal option and consumption strategy for an investor who is obliged to hold a stock position until the time horizon.