A Bank Salvage Model by Impulse Stochastic Controls

Francesco Giuseppe Cordoni, Luca Di Persio and Yilun Jiang
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Francesco Giuseppe Cordoni: Department of Computer Science, University of Verona, Strada le Grazie, 15, 37134 Verona, Italy
Luca Di Persio: Department of Computer Science, University of Verona, Strada le Grazie, 15, 37134 Verona, Italy
Yilun Jiang: Department of Mathematics, Penn State University, University Park, PA 16802, USA

Risks, 2020, vol. 8, issue 2, 1-31

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 < + ∞ .

Keywords: bank salvage model; stochastic impulse control; viscosity solution; inaccessible bankruptcy time; smooth-fit property (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2020
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