Liquidity Risk and Arbitrage Pricing Theory

We shall study the paper by Cetin, Jarrow, Protter, [1]. This pa-per extends classical arbitrage pricing theory to include liquidity risk bystudying an economy where the security’s price depends on the trade size.Extended first and second fundamental theorems of asset pricing are in-vestigated. In an approximately complete market, derivative prices areshown to be the classical arbitrage free price of the derivative plus an ad-justment for the initial liquidity cost of forming the replicating portfolio.The approach to liquidity risk has, as a special case, arbitrage pricingtheory given transaction costs. References[1] Çetin, U., R. Jarrow, P. Protter. 2003, “Liquidity Risk and Arbitrage pricingtheory ”.[2] Delbaen, F. and Schachermayer, W., 1994, “A General Version of the Fun-damental Theorem of Asset Pricing”, Mathematische Annalen, 300 , 463 -520.[3] Harrison, J.M and S. Pliska, 1981, “Martingales and Stochastic Integrals inthe Theory of Continuous Trading,” Stochastic Processes and Their Appli-cations, 11, 215 260.