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A Diffusion Limit for Generalized Correlated Random Walks

  • Urs Gruber (a1) and Martin Schweizer (a2)

Abstract

A generalized correlated random walk is a process of partial sums such that (X, Y) forms a Markov chain. For a sequence (X n ) of such processes in which each takes only two values, we prove weak convergence to a diffusion process whose generator is explicitly described in terms of the limiting behaviour of the transition probabilities for the Y n . Applications include asymptotics of option replication under transaction costs and approximation of a given diffusion by regular recombining binomial trees.

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Copyright

Corresponding author

Postal address: Allianz AG, Allianz Global Risks, Königinstrasse 28, D-80802 München, Germany. Email address: ursgruber@gmx.net
∗∗ Postal address: Departement Mathematik, ETH Zürich, ETH-Zentrum, HG G28.2, CH-8092 Zürich, Switzerland. Email address: martin.schweizer@math.ethz.ch

References

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A Diffusion Limit for Generalized Correlated Random Walks

  • Urs Gruber (a1) and Martin Schweizer (a2)

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