Arbitrage, Hedging and Utility Maximization Using Semi-Static Trading Strategies with American Options
14 Pages Posted: 26 Feb 2015 Last revised: 27 Feb 2015
Date Written: February 26, 2015
We consider a financial model where stocks are available for dynamic trading, and European and American options are available for static trading (semi-static trading strategies). We assume that the American options are infinitely divisible, and can only be bought but not sold. We first get the fundamental theorem of asset pricing (FTAP) using semi-static trading strategies. Using the FTAP result, we further get the dualities for the hedging prices of European and American options. Based on the hedging dualities, we also get the duality for the utility maximization involving semi-static trading strategies.
Keywords: Fundamental theorem of asset pricing, hedging duality, utility maximization, semi-static trading strategies, American options
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