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(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, 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)
(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 ...
(Research report / Forskningsrapport, 2008)
(Research report / Forskningsrapport, 2009)
In this paper we study the Cauchy problem for the wave equation with space-time Lévy noise initial data in the Kondratiev space of stochastic distributions. We prove that this problem has a strong and unique C2-solution, ...
(Research report / Forskningsrapport, 2003)
We give an explicit formula for the Donsker delta function of a certain class of Lévy processes in the Lévy-Hida distribution space. As an application we use the Donsker delta function to derive an explicit chaos expansion ...
(Research report / Forskningsrapport, 2003)
We introduce the forward integral with respect to a pure jump Lévy process and we prove and formula for this integral. Then we use Mallivin calculus to establish a relationship between the forward integral and the Skorohod ...
(Research report / Forskningsrapport, 2009)
In this paper we suggest a general stochastic maximum principle for optimal control of anticipating stochastic differential equations driven by a Lévy type of noise. We use techniques of Malliavin calculus and forward ...
(Research report / Forskningsrapport, 2005)
An insider is an agent who has access to larger information than the one given by the development of the market events and who takes advantage of this in optimizing his position in the market. In this paper we consider the ...