A Bank Salvage Model by Impulse Stochastic Controls

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ID: 110100
2020
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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 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 < + ∞ .
Reference Key
cordoni2020risksa Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Francesco Giuseppe Cordoni;Luca Di Persio;Yilun Jiang;Cordoni, Francesco Giuseppe;Di Persio, Luca;Jiang, Yilun;
Journal risks
Year 2020
DOI
10.3390/risks8020060
URL
https://www.mdpi.com/2227-9091/8/2/60
Keywords
bank salvage model stochastic impulse control viscosity solution inaccessible bankruptcy time smooth-fit property

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