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A Bank Salvage Model by Impulse Stochastic Controls

Author

Listed:
  • 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)

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 < + ∞ .

Suggested Citation

  • Francesco Giuseppe Cordoni & Luca Di Persio & Yilun Jiang, 2020. "A Bank Salvage Model by Impulse Stochastic Controls," Risks, MDPI, vol. 8(2), pages 1-31, June.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:2:p:60-:d:367204
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    References listed on IDEAS

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