Entry-exit decisions with output reduction during exit periods

Yong-Chao Zhang; Yong-Chao Zhang

doi:10.3934/math.2024319

AIMS Mathematics

2024, Volume 9, Issue 3: 6555-6567. doi: 10.3934/math.2024319

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Research article

Entry-exit decisions with output reduction during exit periods

Yong-Chao Zhang ^,

School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Taishan Road 143, Qinhuangdao 066004, China

Received: 03 November 2023 Revised: 20 January 2024 Accepted: 20 January 2024 Published: 06 February 2024
MSC : 60G40, 91B06

In practice, a firm usually reduces the output of a project during exiting the project. We intend to fully analyze the effects of the reduction on the entry-exit decision on the project. To this end, we first obtain the closed expressions of the optimal activating time, optimal start time of the exit, and the maximal expected present value of the project. With these expressions in hand, we completely investigate the effects analytically and numerically. The results show us that the reduction affects the entry-exit decision in different ways due to the different conditions in terms of the parameters involved in the problem. The reduction does not affect the entry-exit decision provided that the firm never exits the project. If the firm exits the project in a finite time, the reduction may postpone or advance the activating time and start time of the exit.
- activating time,
- start time of the exit,
- output reduction,
- optimal stopping problem
Citation: Yong-Chao Zhang. Entry-exit decisions with output reduction during exit periods[J]. AIMS Mathematics, 2024, 9(3): 6555-6567. doi: 10.3934/math.2024319

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Abstract

In practice, a firm usually reduces the output of a project during exiting the project. We intend to fully analyze the effects of the reduction on the entry-exit decision on the project. To this end, we first obtain the closed expressions of the optimal activating time, optimal start time of the exit, and the maximal expected present value of the project. With these expressions in hand, we completely investigate the effects analytically and numerically. The results show us that the reduction affects the entry-exit decision in different ways due to the different conditions in terms of the parameters involved in the problem. The reduction does not affect the entry-exit decision provided that the firm never exits the project. If the firm exits the project in a finite time, the reduction may postpone or advance the activating time and start time of the exit.

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