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Reversible Job-Switching Opportunities and Portfolio Selection

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Abstract

We study an optimal job-switching and consumption/investment problem of an infinitely-lived economic agent who exhibits constant relative risk aversion. We consider two kinds of jobs, one of which allows the agent to receive higher income but makes him suffer higher level of utility loss than the other. The job-switching opportunities are reversible in the sense that one can move from the current job to the other at any time. We provide the closed form solution for the optimal job-switching and consumption/investment policies by using the dynamic programming approach, and show various properties of the solution. We compare the optimal consumption/investment policies to those without job-switching opportunities. As a special case of our problem, we also compare the solution in the case where the agent has a reversible retirement option with that in the case where he has an irreversible retirement option.

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Notes

  1. \(U(c)=\log {c}\) corresponds to the case where \(\gamma = 1\). We do not consider this case here, but similar results can be obtained.

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Acknowledgments

Yong Hyun Shin gratefully acknowledges the support of Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education [NRF-2013R1A1A2058027]. We are indebted to two anonymous referees for helpful comments and kind valuable suggestions to improve our paper essentially.

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Authors and Affiliations

  1. Department of Financial Engineering, Ajou University, Suwon, 16499, Republic of Korea

    Gyoocheol Shim

  2. School of Law, University of Texas at Austin, 78705, Austin, TX, USA

    Jung Lim Koo

  3. Department of Mathematics, Sookmyung Women’s University, Seoul, 04310, Republic of Korea

    Yong Hyun Shin

Authors
  1. Gyoocheol Shim
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  2. Jung Lim Koo
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  3. Yong Hyun Shin
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Correspondence to Yong Hyun Shin.

Additional information

An earlier version of this paper was presented at Korean Financial Management Association 2013 Annual Meeting, Seoul, Korea, November 2, 2013, ICM 2014 Satellite Conference “Mathematical Finance and Control Theory”, Pukyong National University, Busan, Korea, August 23, 2014, and the 1st Conference on Financial and Non-Financial Risk Management, POSTECH, Pohang, Korea, January 29–30, 2015. This paper is an improved version based on that presented with the same title in the above conferences.

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Shim, G., Koo, J.L. & Shin, Y.H. Reversible Job-Switching Opportunities and Portfolio Selection. Appl Math Optim 77, 197–228 (2018). https://doi.org/10.1007/s00245-016-9371-3

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  • DOI: https://doi.org/10.1007/s00245-016-9371-3

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