2022/11/18 by Gergely Bodó, Markus Riedle, Bodó, Gergely +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #28C20 #60G20 #60G52 #60H05 #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2211.10172
openalex publication_date 2022/11/18 · openalex created_date 2022/11/28 · openalex updated_date 2026/07/28
In this work, we introduce a theory of stochastic integration with respect to symmetric α-stable cylindrical Lévy processes. Since α-stable cylindrical Lévy processes do not enjoy a semi-martingale decomposition, our approach is based on a decoupling inequality for the tangent sequence of the Radonified increments. This approach enables us to characterise the largest space of predictable Hilbert-Schmidt operator-valued processes which are integrable with respect to an α-stable cylindrical Lévy process as the collection of all predictable processes with paths in the Bochner space Lα. We demonstrate the power and robustness of the developed theory by establishing a dominated convergence result allowing the interchange of the stochastic integral and limit.