Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Following the framework of Cetin et al. (finance stoch. 8:311-341, 2004),  study the problem of super-replication in the presence of liquidity costs under additional restrictions on the gamma of the hedging strategies in a generalized black-scholes economy.  find that the minimal super-replication price is different from the one suggested by the black-scholes 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. 8:311-341, 2004), who find that the arbitrage-free price of a contingent claim coincides with the Black-Scholes price. Hover, in Cetin et al. (Finance Stoch. 8:311-341, 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).
['Umut Çetin', 'H. Mete Soner', 'Nizar Touzi']
I am writing a research paper on a idea Option hedging for small investors under liquidity costs
[{"from": "human", "value": "I am writing a research paper on a idea Option hedging for small investors under liquidity costs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Following the framework of Cetin et al. (finance stoch. 8:311-341, 2004),  study the problem of super-replication in the presence of liquidity costs under additional restrictions on the gamma of the hedging strategies in a generalized black-scholes economy.  find that the minimal super-replication price is different from the one suggested by the black-scholes 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. 8:311-341, 2004), who find that the arbitrage-free price of a contingent claim coincides with the Black-Scholes price. Hover, in Cetin et al. (Finance Stoch. 8:311-341, 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)."}]