It is well know that the expected exponentially discounted total reward for a
stochastic process can also be defined as the expected total undiscounted
reward earned before an independent exponential stopping time (let us call this
the stopped reward). Feinberg and Fei (2009) recently showed that the variance
of the discounted reward is smaller than the variance of the stopped reward. We
strengthen this result to show that the discounted reward is smaller than the
stopped reward in the convex ordering sense.
Publié le : 2011-03-15
Classification:
Total discounted reward,
stopping time,
stochastic ordering,
60G40,
90C40
@article{1300198151,
author = {Righter, Rhonda},
title = {Stochastic comparison of discounted rewards},
journal = {J. Appl. Probab.},
volume = {48},
number = {1},
year = {2011},
pages = { 293-294},
language = {en},
url = {http://dml.mathdoc.fr/item/1300198151}
}
Righter, Rhonda. Stochastic comparison of discounted rewards. J. Appl. Probab., Tome 48 (2011) no. 1, pp. 293-294. http://gdmltest.u-ga.fr/item/1300198151/