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(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2003)
We give a survey of the stochastic calculus of fractional Brownian motion, and we discuss its applications to financial markets where the prices are described as solutions of stochastic differential equations driven by ...
(Research report / Forskningsrapport, 2002)
In this paper we develop a white noise framework for the study of stochastic partial differential equations driven by a d-parameter (pure jump) Lévy white noise. As an example we use this theory to solve the stochastic ...
(Research report / Forskningsrapport, 2003)
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2002)
We develop a white noise theory for Poisson random measures associated with a Lévy process. The starting point of this theory is a chaos expansion with kernels of polynomial type. We use this to construct the white noise ...
(Research report / Forskningsrapport, 2003)
Multiparameter fractional Brownian motion and quasi-linear stochastic partial differential equations
(Research report / Forskningsrapport, 2000)
(Research report / Forskningsrapport, 2001)
In a market driven by a Lévy martingale, we consider a claim x. We study the problem of minimal variance hedging and we give an explicit formula for the minimal variance portfolio in terms of Malliavin derivatives. We ...