Journal of Applied Probability

Stochastic comparison of discounted rewards

Rhonda Righter

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Abstract

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

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

Dates
First available in Project Euclid: 15 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1300198151

Digital Object Identifier
doi:10.1239/jap/1300198151

Mathematical Reviews number (MathSciNet)
MR2809902

Zentralblatt MATH identifier
1211.60013

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

Keywords
Total discounted reward stopping time stochastic ordering

Citation

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


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