Sadly I have not come across many definitions of heavy tailedness that are compatible with finite support, so I dont have any ready examples of action relevance AND finite support.
Another example involving a momentum-centric definition:
Distributions which are heavy tailed in the sense of not having a finite moment generating function in a neighbourhood of zero heavily reward exploration over exploitation in multi armed bandit scenarios.
See for example an invocation of light tailedness to simplify an analysis at the beginning of this paper, implying that the analysis does not carry over directly to heavy tail scenarios (disclaimer, I have not read the whole thing).
Sadly I have not come across many definitions of heavy tailedness that are compatible with finite support, so I dont have any ready examples of action relevance AND finite support.
Another example involving a momentum-centric definition:
Distributions which are heavy tailed in the sense of not having a finite moment generating function in a neighbourhood of zero heavily reward exploration over exploitation in multi armed bandit scenarios.
See for example an invocation of light tailedness to simplify an analysis at the beginning of this paper, implying that the analysis does not carry over directly to heavy tail scenarios (disclaimer, I have not read the whole thing).