A call option does not have a gradient .. it has a derivative which is a Heaviside function????

I see a disconnect between ISM's question and your answer (caveat: I have a bad dose of flu..)

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Off-topic: I recommend FW in French (published by Gallimard)

Finnegan le Constructeur, stathouder de sa main, maçon des hommes francs, habitait la plus grande rue qu on puisse imarginer en son vieil habit rutilant trop retiré en couleur pour y recevoir des messies, et pendant de nombieuses années cet homme d oiseau, de ciment et d édifices entassa imagifices sur imagifices sur les rives d Hameau Torpeur pour ses foibitants comme dit la chanson.

And the vicus of recirculation from NN to PDE

*erre revie, pass'Evant notre Adame, d'erre rive en rêvière, nous recourante via Vico par chaise percée de recirculation vers Howth Castle et Environs*

ok for the flu ...I understand. What is a bounded variation function ? it is basically a function which derivative is a measure (even if it is a little bit more complex). Consider a call payoff (x-K)^+. Take its derivative : {0, x < K, 1, x > K}, that is a heavyside function, also called a barrier. Then take a second derivative : \delta_{K}(x), that is a dirac, being a measure.

Thanks for the traduction, but it was not a French that I can understand. Thus I ordered Finnegans wake ! I enjoyed reading Ulysse when I lived in Trieste, but it is already quite a technical literature for me !