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Constrained optimal stopping under a regime-switching model

Part of: Mathematical finance Stochastic processes

Published online by Cambridge University Press:  27 March 2024

Takuji Arai  and
Masahiko Takenaka
Takuji Arai*
Affiliation:
Keio University
Masahiko Takenaka*
Affiliation:
Keio University
*
*Postal address: Department of Economics, Keio University, 2-15-45 Mita, Minato-ku, Tokyo, 108-8345, Japan.
*Postal address: Department of Economics, Keio University, 2-15-45 Mita, Minato-ku, Tokyo, 108-8345, Japan.
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Abstract

We investigate an optimal stopping problem for the expected value of a discounted payoff on a regime-switching geometric Brownian motion under two constraints on the possible stopping times: only at exogenous random times, and only during a specific regime. The main objectives are to show that an optimal stopping time exists as a threshold type and to derive expressions for the value functions and the optimal threshold. To this end, we solve the corresponding variational inequality and show that its solution coincides with the value functions. Some numerical results are also introduced. Furthermore, we investigate some asymptotic behaviors.

Keywords

Optimal stoppingregime switchingvariational inequalityreal option

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 91G50: Corporate finance
Type
Original Article
Information
Journal of Applied Probability , Volume 61 , Issue 4 , December 2024 , pp. 1220 - 1239
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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