When opening a book or reading an article on mathematical finance, financial markets (e.g. stock prices) are always modeled by càdlàg semimartingales. I was wondering why it is that these processes are assumed to be càdlàg in the first place since there also exists a theory of stochastic integration for optional semimartingales that are not at all assumed to be càdlàg?
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$\begingroup$ Cadlag is good for prices that move continuously and jump occasionally -- what is your favorite example of a path that is not cadlag but could reasonably be used in a model of stocks? $\endgroup$– user44143Commented Sep 19, 2020 at 13:06
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$\begingroup$ Some process that has a double jump. For example, $X_t := 1_{[0,t_0)} + 2 \cdot 1_{(t_0,T]}$ for $0 < t_0 < T < \infty$. $\endgroup$– vaoyCommented Sep 19, 2020 at 13:22
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$\begingroup$ The initial wording of this question quant.stackexchange.com/questions/27763/… has a striking similarity $\endgroup$– Manfred WeisCommented Sep 19, 2020 at 13:46
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