Mete Soner and Selim Gokay. Superreplication Problem under discrete time Gamma Hedging

Abstract. We consider a financial market consisting of a nonrisky asset and a risky asset. We investigate the discrete time superreplication problem under gamma hedging. We aim to find the initial capital required to superreplicate an European claim under gamma constraint. The gamma constraint puts an upper bound on the sensitivity of the portfolio with respect to changes of the risky asset. We formulate the discrete time problem as a linear program and show there is no dynamic programming to calculate the initial minimum wealth. We use the dynamic programming principle established with the stochastic target formulation of the problem to calculate the minimal starting wealth given the number of stocks we held initially. We develop a fast algorithm to calculate the initial wealth given the initial number of stocks and hence the initial capital to superreplicate the claim.