2015/09/28 by Fred Espen Benth, Benth, Fred Espen, Heidar Eyjolfsson +1
Economics, Econometrics and Finance · Mathematics · #60G20 #60H05 #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Probability (math.PR) #math.PR #msc:60G20 #msc:60H05 #q-fin.MF
paper · pdf · doi:10.48550/arxiv.1509.08272
27 pages
arxiv created 2015/09/28 · arxiv updated 2015/09/29
We lift ambit fields as introduced by Barndorff-Nielsen and Schmiegel to a class of Hilbert space-valued volatility modulated Volterra processes. We name this class Hambit fields, and show that they can be expressed as a countable sum of weighted real-valued volatility modulated Volterra processes. Moreover, Hambit fields can be interpreted as the boundary of the mild solution of a certain first order stochastic partial differential equation. This stochastic partial differential equation is formulated on a suitable Hilbert space of functions on the positive real line with values in the state space of the Hambit field. We provide an explicit construction of such a space. Finally, we apply this interpretation of Hambit fields to develop a finite difference scheme, for which we prove convergence under some Lipschitz conditions.