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Precautionary measures for credit risk management in jump models. (English) Zbl 1288.91187

Summary: Sustaining efficiency and stability by properly controlling the equity to asset ratio is one of the most important and difficult challenges in bank management. Due to unexpected and abrupt decline of asset values, a bank must closely monitor its net worth as well as market conditions, and one of its important concerns is when to raise more capital so as not to violate capital adequacy requirements. In this paper, we model the trade-off between avoiding costs of delay and premature capital raising, and solve the corresponding optimal stopping problem. In order to model defaults in a bank’s loan/credit business portfolios, we represent its net worth by Lévy processes, and solve explicitly for the double exponential jump-diffusion process and for a general spectrally negative Lévy process.

MSC:

91G40 Credit risk
60J75 Jump processes (MSC2010)
60G40 Stopping times; optimal stopping problems; gambling theory
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