Browsing Matematisk institutt by Author "Løkka, Arne"
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Benth, Fred Espen; Løkka, Arne (Research report / Forskningsrapport, 2002)We develop an anticipative calculus for Lévy processes with finite second moment. The calculus is based on the chaos expansion of square-integrable random variables in terms of iterated integrals of the compensated Poisson ...
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Benth, Fred Espen; Di Nunno, Giulia; Løkka, Arne; Øksendal, Bernt; Proske, Frank (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 ...
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Løkka, Arne; Proske, Frank (Research report / Forskningsrapport, 2002)We develop a white noise calculus for pure jump Lévy processes on Poisson space. This theory covers the treatment of Lévy processes of unbounded variation. The starting point of the theory is a novel construction of a ...
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Løkka, Arne; Øksendal, Bernt; Proske, Frank (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 ...
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Løkka, Arne (Research report / Forskningsrapport, 1999)