American options

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

Abstract

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].

Keywords

Strong Solution Risky Asset American Option Obstacle Problem Arbitrage Opportunity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Italia 2011

Authors and Affiliations

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

Personalised recommendations