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 Wloc(1,2),p property is achieved for any 1 < p < +∞.

A bank salvage model by impulse stochastic controls / Cordoni, F.; Di Persio, L.; Jiang, Y.. - In: RISKS. - ISSN 2227-9091. - 8:2(2020), pp. 1-31. [10.3390/risks8020060]

A bank salvage model by impulse stochastic controls

Cordoni F.;Di Persio L.;Jiang Y.
2020

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 Wloc(1,2),p property is achieved for any 1 < p < +∞.
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Cordoni, F.; Di Persio, L.; Jiang, Y.
A bank salvage model by impulse stochastic controls / Cordoni, F.; Di Persio, L.; Jiang, Y.. - In: RISKS. - ISSN 2227-9091. - 8:2(2020), pp. 1-31. [10.3390/risks8020060]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/322946
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