American options

  • Andrea Pascucci
Part of the Bocconi & Springer Series book series (BS)


We present the main results on the pricing and hedging of American derivatives by extending to continuous time the ideas introduced in the discrete-market setting in Section 2.5. Even in the simplest case of the Black-Scholes market model, the hedging and pricing problems for American options need very refined mathematical tools. In the complete-market setting, Bensoussan [41] and Karatzas [198], [199] developed a probabilistic approach based upon the notion of Snell envelope in continuous time and upon the Doob-Meyer decomposition. The problem was also studied by Jaillet, Lamberton and Lapeyre [185] who employed variational techniques, and by Oksendal and Reikvam [273], Gatarek and Świech [149] in the framework of the theory of viscosity solutions. American options for models with jumps were studied among others by Zhang [345], Mulinacci [260], Pham [279], Levendorskii [235], Ekström [119], Ivanov [181], Lamberton and Mikou [227], Bayraktar and Xing [36].


Strong Solution Risky Asset American Option Obstacle Problem Arbitrage Opportunity 
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Copyright information

© Springer-Verlag Italia 2011

Authors and Affiliations

  • Andrea Pascucci
    • 1
  1. 1.Department of MathematicsUniversity of BolognaBologna

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