Measure changes with extinction

We consider a martingale change of measure Q vertical bar(sic), Z(t)P vertical bar(sic) and clarify that in general 1/Z(t) is only a supermartingale under Q. Defining gamma := inf{t >= 0 : Z(t) = 0} as the extinction time, we then give a necessary and sufficient condition Linder which the identity P(gamma = infinity) = P(Z(infinity) > 0) = Q[1/Z(infinity)] holds. (C) 2009 Elsevier B.V. All rights reserved.