Product and Moment Formulas for Iterated Stochastic Integrals\n (associated with L 'evy Processes)

2018/08/31 by Paolo Di Tella, Di Tella, Paolo, Christel Geiß +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #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.1808.10670

openalex publication_date 2018/08/31 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28

Abstract

In this paper, we obtain explicit product and moment formulas for products of\niterated integrals generated by families of square integrable martingales\nassociated with an arbitrary L 'evy process. We propose a new approach applying\nthe theory of compensated-covariation stable families of martingales. Our main\ntool is a representation formula for products of elements of a\ncompensated-covariation stable family, which enables to consider L 'evy\nprocesses, with both jumps and Gaussian part.\n

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