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Unlike financial time series that typically possess fat tails, sub-Gaussian random variables have strong decay in the tails of their distribution. do sub-Gaussian random variables or processes appear in any finance models, or are they useful in financial applications somehow?

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    $\begingroup$ I studied sub-Gaussian RVs at university (some time ago), but due to my lack of interest in them, I didn't learn the theory properly. One thing I do remember: tail convergence theory is not easy. I do recall that all the problem sets on sub-Gaussian RVs were an order of magnitude more difficult than any other topic on the course. I have never encountered the topic during my past 10 years in finance, so my personal conclusion is that the "value to effort" ratio for Sub-Gausian RVs (for finance) is too high. I look forward to what anyone else might have to say on this. $\endgroup$
    – Jan Stuller
    Commented Nov 10, 2020 at 11:10
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    $\begingroup$ @JanStuller, I guess you meant too low. $\endgroup$
    – Richard Hardy
    Commented Nov 10, 2020 at 12:47
  • $\begingroup$ @RichardHardy: yes, you're completely right, I meant to say that in my view, the "value to effort" ratio is too low (in my mind, I was imagining the "effort to value" ratio instead: funny how the mind works :) ). $\endgroup$
    – Jan Stuller
    Commented Nov 10, 2020 at 12:51

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Since a uniform distribution is subgaussian, yes.

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    $\begingroup$ Why the downvotes? $\endgroup$
    – Igor Rivin
    Commented Nov 10, 2020 at 15:43
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    $\begingroup$ Perhaps because you do not explain how the uniform distribution is relevant in finance? $\endgroup$
    – Richard Hardy
    Commented Dec 13, 2020 at 18:21

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