| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 1154391 | Statistics & Probability Letters | 2009 | 5 Pages |
Abstract
We consider a martingale change of measure Q|ℱt≔ZtP|ℱtQ|ℱt≔ZtP|ℱt and clarify that in general 1/Zt1/Zt is only a supermartingale under QQ. Defining Υ≔inf{t≥0:Zt=0}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∞]P(Υ=∞)=P(Z∞>0)=Q[1/Z∞] holds.
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
S.C. Harris, M.I. Roberts,