Publications without Fulltext

Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/3

Browse

Filters

20072

Advanced Search

Filter by

Settings

Department: search.filters.department.Department of MathematicsSubject: search.filters.subject.Economics

Search Results

Now showing 1 - 2 of 2
  • Placeholder
    PublicationMetadata only
    Chapter 6 stochastic representations for nonlinear parabolic pdes
    (Elsevier, 2007) Department of Mathematics; Department of Mathematics; Soner, Halil Mete; Faculty Member; College of Sciences; N/A
    We discuss several different representations of nonlinear parabolic partial differential equations in terms of Markov processes. After a brief introduction of the linear case, different representations for nonlinear equations are discussed. One class of representations is in terms of stochastic control and differential games. An extension to geometric equations is also discussed. All of these representations are through the appropriate expected values of the data. Different type of representations are also available through backward stochastic differential equations. A recent extension to second-order backward stochastic differential equations allow us to represent all fully nonlinear scalar parabolic equations.
  • Placeholder
    PublicationMetadata only
    Hedging under gamma constraints by optimal stopping and face-lifting
    (Blackwell Publishing, 2007) Touzi, Nizar; Department of Mathematics; Department of Mathematics; Soner, Halil Mete; Faculty Member; College of Sciences; N/A
    A super-replication problem with a gamma constraint, introduced in Soner and Touzi, is studied in the context of the one-dimensional Black and Scholes model. Several representations of the minimal super-hedging cost are obtained using the characterization derived in Cheridito, Soner, and Touzi. It is shown that the upper bound constraint on the gamma implies that the optimal strategy consists in hedging a conveniently face-lifted payoff function. Further an unusual connection between an optimal stopping problem and the lower bound is proved. A formal description of the optimal hedging strategy as a succession of periods of classical Black-Scholes hedging strategy and simple buy-and-hold strategy is also provided.