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Stochastic Comparison of Discounted Rewards

Published online by Cambridge University Press:  14 July 2016

Rhonda Righter*
Affiliation:
University of California
*
Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA. Email address: [email protected]
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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.

Type
Research Article
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, 12091212.Google Scholar