Displaying similar documents to “A sharp maximal inequality for continuous martingales and their differential subordinates”

Embedding of random vectors into continuous martingales

E. Dettweiler (1999)

Studia Mathematica

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Let E be a real, separable Banach space and denote by L 0 ( Ω , E ) the space of all E-valued random vectors defined on the probability space Ω. The following result is proved. There exists an extension Ω ˜ of Ω, and a filtration ( ℱ ˜ t ) t ≥ 0 on Ω ˜ , such that for every X ∈ L 0 ( Ω , E ) there is an E-valued, continuous ( ℱ ˜ t ) -martingale ( M t ( X ) ) t ≥ 0 in which X is embedded in the sense that X = M τ ( X ) a.s. for an a.s. finite stopping time τ. For E = ℝ this gives a Skorokhod embedding for all X ∈ L 0 ( Ω , ℝ ) , and for general E this leads to a representation of random...

Hedging in complete markets driven by normal martingales

Youssef El-Khatib, Nicolas Privault (2003)

Applicationes Mathematicae

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This paper aims at a unified treatment of hedging in market models driven by martingales with deterministic bracket ⟨ M , M ⟩ t , including Brownian motion and the Poisson process as particular cases. Replicating hedging strategies for European, Asian and Lookback options are explicitly computed using either the Clark-Ocone formula or an extension of the delta hedging method, depending on which is most appropriate.