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Simple question of a curious person:

One can say that prices tend to rise "slowly" and drop "all of a sudden". Still, they are a geometric composition upon random returns.

As I understand, this is not a feature of a geometric brownian motion.

If so, what would be a standard price process consistent with this behavior?

Best!

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    $\begingroup$ Sounds like you want a jump-diffusion process. Lots of material available online $\endgroup$ – James Spencer-Lavan Oct 19 '18 at 18:17
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The natural extension of Brownian motion that includes jump are called Levy processes

https://en.wikipedia.org/wiki/L%C3%A9vy_process

probably you want to look into those.

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