  Diffusion in a linear potential in the presence of position-dependent killing
is used to mimic a default process. Different assumptions regarding transport
coefficients, initial conditions, and elasticity of the killing measure lead to
diverse models of bankruptcy. One "stylized fact" is fundamental for our
consideration: empirically default is a rather rare event, especially in the
investment grade categories of credit ratings. Hence, the action of killing may
be considered as a small parameter. In a number of special cases we derive
closed-form expressions for the entire term structure of the cumulative
probability of default, its hazard rate and intensity. Comparison with
historical data on global corporate defaults confirms applicability of the
model-independent perturbation method for companies in the investment grade
categories of credit ratings and allows for
