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Hedging in complete markets driven by normal martingales

Youssef El-Khatib, Nicolas Privault (2003)

Applicationes Mathematicae

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.

Hiding a constant drift

Vilmos Prokaj, Miklós Rásonyi, Walter Schachermayer (2011)

Annales de l'I.H.P. Probabilités et statistiques

The following question is due to Marc Yor: Let B be a brownian motion and St=t+Bt. Can we define an -predictable process H such that the resulting stochastic integral (H⋅S) is a brownian motion (without drift) in its own filtration, i.e. an -brownian motion? In this paper we show that by dropping the requirement of -predictability of H we can give a positive answer to this question. In other words, we are able to show that there is a weak solution to Yor’s question. The original question, i.e.,...

Hitting time of a corner for a reflected diffusion in the square

F. Delarue (2008)

Annales de l'I.H.P. Probabilités et statistiques

We discuss the long time behavior of a two-dimensional reflected diffusion in the unit square and investigate more specifically the hitting time of a neighborhood of the origin. We distinguish three different regimes depending on the sign of the correlation coefficient of the diffusion matrix at the point 0. For a positive correlation coefficient, the expectation of the hitting time is uniformly bounded as the neighborhood shrinks. For a negative one, the expectation explodes in a polynomial way...

Homogenization of a semilinear parabolic PDE with locally periodic coefficients: a probabilistic approach

Abdellatif Benchérif-Madani, Étienne Pardoux (2007)

ESAIM: Probability and Statistics

In this paper, a singular semi-linear parabolic PDE with locally periodic coefficients is homogenized. We substantially weaken previous assumptions on the coefficients. In particular, we prove new ergodic theorems. We show that in such a weak setting on the coefficients, the proper statement of the homogenization property concerns viscosity solutions, though we need a bounded Lipschitz terminal condition.

Homogenization of locally stationary diffusions with possibly degenerate diffusion matrix

Rémi Rhodes (2009)

Annales de l'I.H.P. Probabilités et statistiques

This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic one and a smoothly varying macroscopic one. The homogenization procedure aims to give a macroscopic approximation that takes into account the microscopic heterogeneities. This paper follows [Probab. Theory Related Fields (2009)] and improves this latter work by...

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