Description: A study of the effect of random interest rates on life insurance programs and on annuities both certain and non-certain. This is done under several assumptions on the stochastic structure of the interest rates.

Description: Studies default risk through the two-sided exit problem of a time-homogeneous di§usion process with tax payments of loss-carry-forward type and obtains explicit formulas for the exit probabilities. If the lower boundary is understood as the default threshold, then the nondefault probability is solved as a special case. A sufficient and necessary condition for the tax identity is discovered.