摘要：The present paper is devoted to the study of a ibank salvage model/i 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 iquasi-variational inequality/i (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 inline-formula math display="inline" semantics msubsup miW/mi mrow mil/mi mio/mi mic/mi /mrow mrow mo(/mo mn1/mn mo,/mo mn2/mn mo)/mo mo,/mo mip/mi /mrow /msubsup /semantics /math /inline-formula property is achieved for any inline-formula math display="inline" semantics mrow mn1/mn mo/mo mip/mi mo/mo mo+/mo mi∞/mi /mrow /semantics /math /inline-formula.
