Journal of Applied Probability

Stochastic comparison of discounted rewards

Rhonda Righter

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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.

Article information

J. Appl. Probab., Volume 48, Number 1 (2011), 293-294.

First available in Project Euclid: 15 March 2011

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 90C40: Markov and semi-Markov decision processes

Total discounted reward stopping time stochastic ordering


Righter, Rhonda. Stochastic comparison of discounted rewards. J. Appl. Probab. 48 (2011), no. 1, 293--294. doi:10.1239/jap/1300198151.

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