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Measure changes with extinction
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Harris, S.C. and Roberts, Matthew Iain (2009) Measure changes with extinction. Statistics & Probability Letters, Vol.79 (No.8). pp. 1129-1133. doi:10.1016/j.spl.2008.12.025 ISSN 0167-7152.
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Official URL: http://dx.doi.org/10.1016/j.spl.2008.12.025
Abstract
We consider a martingale change of measure Q|ℱt≔ZtP|ℱt and clarify that in general 1/Zt is only a supermartingale under Q. Defining Υ≔inf{t≥0:Zt=0} as the extinction time, we then give a necessary and sufficient condition under which the identity P(Υ=∞)=P(Z∞>0)=Q[1/Z∞] holds.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Statistics & Probability Letters | ||||
Publisher: | Elsevier Science BV | ||||
ISSN: | 0167-7152 | ||||
Official Date: | 2009 | ||||
Dates: |
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Volume: | Vol.79 | ||||
Number: | No.8 | ||||
Page Range: | pp. 1129-1133 | ||||
DOI: | 10.1016/j.spl.2008.12.025 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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