Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimally stopping at a given distance from the ultimate supremum of a
  spectrally negative L\'evy process   We consider the optimal prediction problem of stopping a spectrally negative
L\'evy process as close as possible to a given distance $b \geq 0$ from its
ultimate supremum, under a squared error penalty function. Under some mild
conditions, the solution is fully and explicitly characterised in terms of
scale functions. We find that the solution has an interesting non-trivial
structure: if $b$ is larger than a certain threshold then it is optimal to stop
as soon as the difference between the running supremum and the position of the
process exceeds a certain level (less than $b$), while if $b$ is smaller than
this threshold then it is optimal to stop immediately (independent of the
running supremum and position of the process). We also present some examples.

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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con