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Markovian representations of fractional Brownian motion and some applications in mathematical finance

Oberseminar Finanz- und Versicherungsmathematik


Markovian representations of fractional Brownian motion and
some applications in mathematical finance

Abstract


A wide class of Gaussian processes, including fractional
Brownian motion, can be represented as linear functions of an
infinite-dimensional affine process. This opens the door to analyzing
such processes using tools from Markov processes and SPDEs. Moreover,
the affine structure makes computations tractable, and the
representation lends itself to numerical implementation. We will look
into some of this theory and its applications in mathematical finance.