Optimal hedging with leverage constraints and transaction costs: A discrete time approach

This thesis considers the problem of hedging a given state-contingent payoff under market imperfections. The imperfections considered are leverage constraints (borrowing and short-selling constraints) and transaction costs. In this study linear programming techniques are applied since traditional pricing models cannot be used in the given situation. The smallest initial wealth along with a corresponding trading strategy is determined which suffices to generate enough cash flow to satisfy the contracted liability in every state. Under both market imperfections, hedging cost are significantly higher than in the unconstrained situation. Also, the constrained hedging strategy is found to be less aggressive. The paper also shows that imposing either of the given imperfections, when the other one is already present, has only a small effect.