  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 tradeoff 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 Levy processes, and solve
explicitly for the double exponential jump diffusion process and for a general
spectrally negative Levy process.
