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Keywords = inaccessible bankruptcy time

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31 pages, 526 KiB  
Article
A Bank Salvage Model by Impulse Stochastic Controls
by Francesco Giuseppe Cordoni, Luca Di Persio and Yilun Jiang
Risks 2020, 8(2), 60; https://doi.org/10.3390/risks8020060 - 4 Jun 2020
Cited by 1 | Viewed by 3144
Abstract
The present paper is devoted to the study of a bank salvage model with a finite time horizon that is subjected to stochastic impulse controls. In our model, the bank’s default time is a completely inaccessible random quantity generating its own filtration, then [...] Read more.
The present paper is devoted to the study of a bank salvage model with a finite time horizon that is subjected to stochastic impulse controls. In our model, the bank’s default time is a completely inaccessible random quantity generating its own filtration, then reflecting the unpredictability of the event itself. In this framework the main goal is to minimize the total cost of the central controller, which can inject capitals to save the bank from default. We address the latter task, showing that the corresponding quasi-variational inequality (QVI) admits a unique viscosity solution—Lipschitz continuous in space and Hölder continuous in time. Furthermore, under mild assumptions on the dynamics the smooth-fit W l o c ( 1 , 2 ) , p property is achieved for any 1 < p < + . Full article
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