A lending scheme for a system of interconnected banks with probabilistic constraints of failure

Cordoni, Francesco; Persio, Luca Di; Prezioso, Luca

doi:10.48550/arxiv.1903.06042

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“…Typical example are default triggered by some stopping time defined as a hitting time. Such an approach has been for instance considered in [14,15,35]. The latter instead considers a default event which is completely inaccessible for the probabilistic reference filtration, so that in order to solve the problem the typical approach is to rely on filtration enlargment techniques, see, e.g., [6,40].…”

Section: Introductionmentioning

confidence: 99%

“…The main contribution of the present paper is to develop a concrete financial setting that models the evolution of a financial entity, controlled by an external supervisor who is willing to lend money in order to maximize a given utility function; see also [11,15,20,35,43] for setting in which a financial supervisor aims at controlling a system of banks of general financial entities. In compete generality, we will assume that the financial entity may fail at some random time that is inaccessible to the reference filtration, which represents the controller knowledge.…”

Section: Introductionmentioning

confidence: 99%

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A bank salvage model by impulse stochastic controls

Cordoni¹,

Persio²,

Jiang³

2019

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The present paper is devoted to the study of a bank salvage model with finite time horizon and 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 who can inject capitals to save the bank from default. We address the latter task showing that the corresponding quasivariational 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(1,2),p loc property is achieved for any 1 < p < +∞.

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