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The It{ô}-Föllmer formula -- nonstandard cases
W. M. Bednorz, R. M. Łochowski, P. L. Zondi +2
The purpose of this note is to prove the It{ô}-Föllmer formula for the càdlàg paths possessing quadratic variation in a possibly ``weakest'' sense along some sequence of partitions…
Sensitivity analysis of path-dependent options in an incomplete market with pathwise functional Ito calculus
Siboniso Confrence Nkosi, Farai Julius Mhlanga
Functional It^o calculus is based on an extension of the classical It^o calculus to functionals depending on the entire past evolution of the underlying paths and not only on its c…
Quadratic variation and local times of the horizontal component of the Peano curve (square filling curve)
Phumlani L. Zondi, Darlington Hove, Rafał M. Łochowski +1
We show that the horizontal component of the Peano curve has quadratic variation equal the limit of quadratic variations along the Lebesgue partitions for grids of the form $3^{-n}…