Arbitrage, hedging and utility maximization using semi-static trading strategies with American options

Erhan Bayraktar, Zhou Zhou

    Research output: Contribution to journalArticlepeer-review

    4 Scopus citations

    Abstract

    We consider a financial market 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. In the first part of the paper, we work within the framework without model ambiguity. We first get the fundamental theorem of asset pricing (FTAP). Using the FTAP, we 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. In the second part of the paper, we consider the market which admits nondominated model uncertainty. We first establish the hedging result, and then using the hedging duality we further get the FTAP. Due to the technical difficulty stemming from the nondominancy of the probability measure set, we use a discretization technique and apply the minimax theorem.

    Original languageEnglish (US)
    Pages (from-to)3531-3558
    Number of pages28
    JournalAnnals of Applied Probability
    Volume26
    Issue number6
    DOIs
    StatePublished - Dec 2016

    Bibliographical note

    Funding Information:
    Supported in part by NSF Grant DMS-09-55463.

    Publisher Copyright:
    © Institute of Mathematical Statistics, 2016.

    Keywords

    • American options
    • Fundamental theorem of asset pricing
    • Hedging duality
    • Semi-static trading strategies
    • Utility maximization

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