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Stochastic Comparison of Discounted Rewards

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Rhonda Righter
Rhonda Righter*
Affiliation:
University of California
*
∗Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA. Email address: rrighter@ieor.berkeley.edu
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Abstract

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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.

Keywords

Total discounted rewardstopping timestochastic ordering

MSC classification

Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory 90C40: Markov and semi-Markov decision processes
Type
Research Article
Information
Journal of Applied Probability , Volume 48 , Issue 1 , March 2011 , pp. 293 - 294
Copyright
Copyright © Applied Probability Trust 2011 

References

Feinberg, E. A. and Fei, J. (2009). An inequality for variances of the discounted rewards. J. Appl. Prob. 46, 1209–1212.Google Scholar