Speaker: Masahiko Egami, Kyoto University

Title: Precautionary Measures for Credit Risk Management in Jump Models

Abstract:
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 appropriate L´evy 
processes, and solve explicitly for the double exponential jump diffusion 
process. In particular, for the spectrally negative case, we generalize the 
formulation using the scale function, and obtain explicitly the optimal 
solutions for the exponential jump diffusion process.