Optimal Stopping When the Absorbing Boundary is Following After

14 Pages Posted: 3 Aug 2013

See all articles by Masahiko Egami

Masahiko Egami

Kyoto University

Tadao Oryu

Kyoto University - Graduate School of Economics

Date Written: July 31, 2013

Abstract

We consider a new type of optimal stopping problems where the absorbing boundary moves as the state process X attains new maxima S. More specifically, we set the absorbing boundary as S-b where b is a certain constant. This problem is naturally connected with excursions from zero of the reflected process S-X. The problem is in nature a two-dimensional one. It turns out that we can reduce the original problem to an infinite number of one-dimensional optimal stopping problems, and we find explicit solutions. This work is motivated by the bank's profit maximization with the constraint that it maintain a certain level of leverage ratio. When the bank's asset value severely deteriorates, the bank's required capital requirement shall be violated. This situation corresponds to X

Keywords: High leverage, Bank Failure, Optimal stopping, excursion theory

JEL Classification: C61, G21

Suggested Citation

Egami, Masahiko and Oryu, Tadao, Optimal Stopping When the Absorbing Boundary is Following After (July 31, 2013). Available at SSRN: https://ssrn.com/abstract=2305146 or http://dx.doi.org/10.2139/ssrn.2305146

Masahiko Egami (Contact Author)

Kyoto University ( email )

Yoshida-Honmachi
Sakyo-ku
Kyoto, 606-8501
Japan

Tadao Oryu

Kyoto University - Graduate School of Economics ( email )

Japan

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