Option hedging for small investors under liquidity costs Following the framework of Cetin et al. (finance stoch. 8:311341, 2004), we study the problem of superreplication in the presence of liquidity costs under additional restrictions on the gamma of the hedging strategies in a generalized blackscholes economy. We find that the minimal superreplication price is different from the one suggested by the blackscholes formula and is the unique viscosity solution of the associated dynamic programming equation. This is in contrast with the results of Cetin et al. (Finance Stoch. 8:311341, 2004), who find that the arbitragefree price of a contingent claim coincides with the BlackScholes price. However, in Cetin et al. (Finance Stoch. 8:311341, 2004) a larger class of admissible portfolio processes is used, and the replication is achieved in the L (2) approximating sense. JEL (C61  G13  D52).

Portfolio problems with two levels decisionmakers: Optimal portfolio selection with pricing decisions on transaction costs Abstract   This paper presents novel bilevel leaderfollower portfolio selection problems in which the financial intermediary becomes a decisionmaker. This financial intermediary decides on the unit transaction costs for investing in some securities, maximizing its benefits, and the investor chooses his optimal portfolio, minimizing risk and ensuring a given expected return. Hence, transaction costs become decision variables in the portfolio problem, and two levels of decisionmakers are incorporated: the financial intermediary and the investor. These situations give rise to general Nonlinear Programming formulations in both levels of the decision process. We present different bilevel versions of the problem: financial intermediaryleader, investorleader, and social welfare; besides, their properties are analyzed. Moreover, we develop Mixed Integer Linear Programming formulations for some of the proposed problems and effective algorithms for some others. Finally, we report on some computational experiments performed on data taken from the Dow Jones Industrial Average, and analyze and compare the results obtained by the different models.