Optimal Stopping When the Absorbing Boundary is Following After
| Autor: | Masahiko Egami, Tadao Oryu |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | SSRN Electronic Journal. |
| ISSN: | 1556-5068 |
| DOI: | 10.2139/ssrn.2305146 |
| Popis: | 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. We examine this constrained optimization with the state variable X as a spectrally negative Levy process. The problem is in nature a two-dimensional one. The threshold strategy given by the path of X is not in fact optimal. It turns out, however, 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 Comment: 21 pages, 11 figures |
| Databáze: | OpenAIRE |
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