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- W3157409712 abstract "This work is concerned with forest and cumulant type expansions of general random variables on a filtered probability spaces. We establish a “broken exponential martingale” expansion that generalizes and unifies the exponentiation result of Alos, Gatheral, and Radoicic (SSRN’17; [AGR20]) and the cumulant recursion formula of Lacoin, Rhodes, and Vargas (arXiv; [LRV19]). Specifically, we exhibit the two previous results as lower dimensional projections of the same generalized forest expansion, subsequently related by forest reordering. Our approach also leads to sharp integrability conditions for validity of the cumulant formula, as required by many of our examples, including iterated stochastic integrals, Levy area, Bessel processes, KPZ with smooth noise, Wiener-Ito chaos and “rough” stochastic (forward) variance models." @default.
- W3157409712 created "2021-05-10" @default.
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- W3157409712 date "2020-01-01" @default.
- W3157409712 modified "2023-10-05" @default.
- W3157409712 title "Forests, Cumulants, Martingales" @default.
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- W3157409712 doi "https://doi.org/10.2139/ssrn.3620174" @default.
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