A sharp maximal inequality for continuous martingales and their differential subordinates

Adam Osękowski

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 $\tilde{Ω}$ of Ω, and a filtration ${({\tilde{ℱ}}_{t})}_{t \geq 0}$ on $\tilde{Ω}$ , such that for every $X \in L^{0} (Ω, E)$ there is an E-valued, continuous $({\tilde{ℱ}}_{t})$ -martingale ${(M_{t} (X))}_{t \geq 0}$ 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 $X \in L^{0} (Ω, ℝ)$ , and for general E this leads to a representation of random...

Some remarks on the martingales satisfying the structure equation ${[X, X]}_{t} = t + \int_{0}^{t} β X_{s^{-}} d X_{s}$

Tsung Ming Chao, Ching Sung Chou (2001)

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P. Mc Gill (1986)

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Norihiko Kazamaki (1985)

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Séminaire de probabilités de Strasbourg

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Michel Émery (1989)

Séminaire de probabilités de Strasbourg

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Edwin Perkins (1985)

Séminaire de probabilités de Strasbourg

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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.

A note on $L_{2}$ maximal inequalities

Jim Pitman (1981)

Séminaire de probabilités de Strasbourg

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